Cell State Identification by Mass, Density, and
Volume
by
Andrea K. Bryan
Bioengineering, B.S.,
University of California, San Diego (2005)
Submitted to the Department of Biological Engineering
in partial fulfillment of the requirements for the degree of
Doctor of Philosophy in Biological Engineering
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2011
c Massachusetts Institute of Technology 2011. All rights reserved.
Author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Department of Biological Engineering
April 29, 2011
Certified by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Scott R. Manalis
Professor
Thesis Supervisor
Accepted by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
K. Dane Wittrup
Chairman, Department Committee on Graduate Theses
2
Cell State Identification by Mass, Density, and Volume
by
Andrea K. Bryan
Submitted to the Department of Biological Engineering
on April 29, 2011, in partial fulfillment of the
requirements for the degree of
Doctor of Philosophy in Biological Engineering
Abstract
Cell size is often overlooked in the drive to define molecular mechanisms, but as a basic
physical property it is an integrator of the cell’s metabolic rate and indicator of cell
fate. Development of the Suspended Microchannel Resonator (SMR), a microfluidic
mass measurement system, enables femtogram cell mass resolution, and the resistive
pulse (Coulter) technique provides high-speed electronic readout of cell volume. With
these tools, we developed four methods to measure cell density, the ratio of mass to
volume.
We first measure the average density of cell populations using the SMR and a
Coulter counter. We observe that cell density increases prior to bud formation at the
G1/S transition of budding yeast, which is consistent with previous measurements
using density gradient centrifugation. To investigate the origin of this density increase,
we use the SMR to measure buoyant mass in high density media and monitor relative
density changes of growing yeast cells. We find that the density increase requires
energy, function of the protein synthesis regulator TOR, passage through START,
and an intact actin cytoskeleton. These techniques are suitable for most non-adherent
cells and subcellular particles to characterize cell growth in a variety of applications.
We next develop two platforms to measure single-cell mass, volume, and density.
These properties are calculated from two SMR buoyant mass measurements, each
in different density fluids. These measurements are achieved by serially connecting
two SMR structures through a microchannel with an intermediate T-junction, such
that a cell is measured by each SMR in different density fluids. Similar measurements can also be made with one SMR by reversing the SMR fluid flow after a cell
is measured—each cell re-enters the SMR in a higher density fluid for a second measurement. We find that the intrinsic cell-to-cell density variation is nearly 100-fold
smaller than the mass or volume variation, and by simultaneously measuring density
and mass, we identify distinct subpopulations of diseased and healthy cells that are
indistinguishable by mass or volume alone.
Thesis Supervisor: Scott R. Manalis
Title: Professor
3
4
Acknowledgments
First and foremost, I would like to thank Scott for being the greatest adviser. Scott
has offered guidance on nearly every aspect of academic life—project direction, grant
writing, ethics, hiring—and with great willingness. He has tremendous understanding
of the research process from a student’s perspective and is eager to discover collaborations and apply our work to new and expanding fields. We have had and I have been
included in conversations with amazing depth, but my experience has been so much
more. Thank you Scott. I hope one day that I too build my “road for a thousand
trucks.”
In the same way that Scott has guided me in more than project direction, our
collaborators had a major part in my academic development. Angelika has an amazing confidence in me, and great understanding of the balance between biology and
engineering. Alexi, from Angelika’s lab, gave not only significant time to our collaboration, but also careful thought. Among many things, Alexi taught me that “the
best experiment is the one that you can do,” which is useful advice when faced with
a daunting number of unknowns and tools in biological research. Marc Kirschner,
Subra Suresh, and Doug Lauffenberger are powerful scientific role models for me
and have each afforded the Manalis lab many opportunities.
This would not be complete without thanking all of the Manalis lab, past and
present, and a few members in particular. Thomas entertained the ever-naı̈ve pitches
of a beginning graduate student (and built the first SMR!). Scott K should certainly
be co-author of my unwritten thesis chapter titled “Lab ordering and tours,” and we
have become great friends along the way. Will is incredibly detail-oriented and,
combined with his knowledge of the right tool for every job, makes each day working
with him a pleasure.
Thank you to everyone who created my life outside the lab. You all have coached
me through the ups and downs in so many ways, and it is amazing how a few words
can set one off in such an amazing direction. My parents and the experiences they
gave me are the foundation from which all of this grew. My girlfriends, Anusuya and
5
Bahar, and I share in graduate life experiences and we have commiserated over tea,
cookies, and great movies. My animals (Martin, Ludwig, and Emma) are my most
welcome distractions and patient listeners. And, of course, I need to thank Garnet
for not only making me the best lunches of anyone on campus, but for putting up
with my technical diatribes on microfluidics, the SMR, and cell density. Thank you
for all that you do.
6
Contents
1 Introduction
1.1
1.2
17
Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17
1.1.1
Cell density fundamentals . . . . . . . . . . . . . . . . . . . .
17
1.1.2
Methods to measure cell size and density . . . . . . . . . . . .
18
SMR description and measurements . . . . . . . . . . . . . . . . . . .
22
1.2.1
Device concept and basic operation . . . . . . . . . . . . . . .
22
1.2.2
Buoyant mass as a physical property to characterize single cells
26
2 Average and relative cell density measurements with the SMR
2.1
2.2
2.3
29
Density, volume, and buoyant mass of growth-arrested cells . . . . . .
30
2.1.1
32
Yeast density is coordinated with the cell cycle . . . . . . . . .
Continuous buoyant mass and volume measurements of synchronized
cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
36
Single-cell relative density measurements in Percoll medium . . . . .
38
2.3.1
The G1/S density change in yeast . . . . . . . . . . . . . . . .
39
2.3.2
The change in yeast density at G1/S requires energy, TOR
function, passage through START, and an intact cytoskeleton
41
2.4
Conclusions and Future Directions
. . . . . . . . . . . . . . . . . . .
43
2.5
Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . .
44
3 Single-cell density measurements with a dual SMR
3.1
47
Dual SMR concept and design . . . . . . . . . . . . . . . . . . . . . .
47
3.1.1
50
Fluidic mixing in microchannels . . . . . . . . . . . . . . . . .
7
3.1.2
Cantilever crosstalk . . . . . . . . . . . . . . . . . . . . . . . .
53
3.2
Dual SMR operation and fluidic control . . . . . . . . . . . . . . . . .
54
3.3
Data processing: Measurement concept and peak pairing . . . . . . .
55
3.4
Sources of measurement error . . . . . . . . . . . . . . . . . . . . . .
60
3.4.1
Effect of fluid density choices on measurement error . . . . . .
61
3.4.2
Measurement of dual SMR density resolution
63
3.5
. . . . . . . . .
Cytokine-deprivation causes cell atrophy, apoptosis, and changes in
density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
64
3.5.1
Background . . . . . . . . . . . . . . . . . . . . . . . . . . . .
64
3.5.2
Cell density as a function of starvation . . . . . . . . . . . . .
65
4 Single cell density identifies cell state
4.1
4.2
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
69
4.1.1
A microfluidic implementation of Archimedes’ method . . . .
71
Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . .
71
4.2.1
Single particle mass, density, and volume . . . . . . . . . . . .
71
4.2.2
Erythrocyte density is determined by more than environmental
conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
76
Density identifies early stages of apoptosis . . . . . . . . . . .
78
Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . .
80
4.2.3
4.3
5 SMR system development and analysis details
5.1
69
87
Peak height determination for buoyant mass measurement: fitting and
filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
87
5.2
Fluid density calibration and density measurement of an arbitrary fluid 89
5.3
Correction of buoyant mass to a fluid density standard using average
cell volume
5.4
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
91
Density variation estimate from mean buoyant mass and volume by
the Geary-Hinkley Transformation
. . . . . . . . . . . . . . . . . . .
92
5.5
Post-fabrication KOH etch for silicon microchannels . . . . . . . . . .
93
5.6
SMR fluidic control to eliminate size biasing . . . . . . . . . . . . . .
96
8
5.7
Choice of a biologically-compatible high density medium . . . . . . .
98
5.8
SMR particle position-dependent error . . . . . . . . . . . . . . . . . 100
6 Postscript
105
A Supplementary Figures
107
A.1 Chapter 2 Supplementary Figures . . . . . . . . . . . . . . . . . . . . 107
A.2 Chapter 3 Supplementary Figures . . . . . . . . . . . . . . . . . . . . 113
9
10
List of Figures
1-1 Sample density gradient . . . . . . . . . . . . . . . . . . . . . . . . .
19
1-2 Illustration of instrument and cell measurement . . . . . . . . . . . .
23
1-3 Fluidic and electronic schematic of the SMR system . . . . . . . . . .
24
2-1 Cell density, mass, and volume measurement concept . . . . . . . . .
31
2-2 Density, buoyant mass, and volume of cells synchronized by cell cycle
blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
2-3 Density, buoyant mass, and volume of cells synchronized by elutriation
35
2-4 Buoyant mass and volume growth rates are cell cycle-dependent . . .
37
2-5 Real-time relative cell density measurement concept . . . . . . . . . .
38
2-6 Changes in cell density require energy, TOR function, passage through
START, and an intact cytoskeleton. . . . . . . . . . . . . . . . . . . .
40
3-1 Concept for single cell mass, density, and volume measurement . . . .
48
3-2 Illustration of dual SMR instrument . . . . . . . . . . . . . . . . . . .
49
3-3 Illustration of dual SMR T-junction . . . . . . . . . . . . . . . . . . .
50
3-4 Fluid mixing as a function of time and channel width . . . . . . . . .
51
3-5 Sample baseline instabilities in the second cantilever of the dual SMR
52
3-6 Frequency trace and theoretical frequency response for two 15x20 µm
cantilevers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
53
3-7 Fluidic schematic for dual SMR . . . . . . . . . . . . . . . . . . . . .
54
3-8 Comparison between dual SMR peak pairing and the Needleman-Wunsch
algorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
57
3-9 Example of two accepted peak pairs from the dual SMR . . . . . . .
59
11
3-10 Geometric display of dual SMR scoring matrix . . . . . . . . . . . . .
60
3-11 The choice of fluid density affects the accuracy to which particle properties may be calculated. . . . . . . . . . . . . . . . . . . . . . . . . .
62
3-12 Polystyrene bead density measured with the dual SMR . . . . . . . .
63
3-13 FL5.12 cell density and volume upon cytokine-deprivation . . . . . .
66
4-1 Applying Archimedes’ method to measure single cell mass, volume,
and density. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
72
4-2 Illustration of single cell mass, density, and volume measurement using
a single SMR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
73
4-3 Sample mass, density, volume measurement frequency trace for a 15x20µm
SMR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
74
4-4 Measuring the mass, volume, and density distributions of beads, malariainfected erythrocytes, and transfusion recipients with thalassemia and
sickle-cell anemia . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
75
4-5 Single-cell mass, volume, and density distribution widths for transfusion patients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
77
4-6 Single-cell mass, volume, and density of L1210 mouse lymphocytic
leukemia cells during treament with staurosporine . . . . . . . . . . .
79
5-1 Peak defined by the analytical function and smoothed with a SavitzkyGolay filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
88
5-2 Fluid density calibration before and after KOH etching . . . . . . . .
94
5-3 Frequency response during post-fabrication KOH etching . . . . . . .
95
5-4 Illustration of SMR channel bifurcation . . . . . . . . . . . . . . . . .
97
5-5 Budding yeast volume distributions before and after SMR measurements 97
5-6 Illustration of position-dependent error . . . . . . . . . . . . . . . . . 100
5-7 Position-dependent error simulations . . . . . . . . . . . . . . . . . . 102
5-8 Histograms of relative resonance frequency shifts for a population and
single trapped particle . . . . . . . . . . . . . . . . . . . . . . . . . . 103
12
A-1 Proportion of budded cells for Figure 2-4 measurements. . . . . . . . 108
A-2 Statistical analysis of continuous measurement shown in Figure 2-4
measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
A-3 Buoyant mass and volume of additional continuous measurement. . . 110
A-4 Statistical analysis of continuous measurement shown in Supplemental
Figure A-3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
A-5 Bud emergence and DNA content analysis. . . . . . . . . . . . . . . . 112
A-6 Diagram of density measurement system . . . . . . . . . . . . . . . . 113
A-7 Additional statistical analysis of erythrocyte mass, volume, and density
distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
A-8 Comparisons between the Siemens ADVIA clinical hematology instrument and our SMR . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
A-9 Comparisons between the Siemens ADVIA clinical hematology instrument and our SMR . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
A-10 Correlations among the distribution widths of erythrocyte volumes,
masses, and densities . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
A-11 Analysis of repeated blood draws from a transfused thalassemia patient 118
13
14
List of Tables
1.1
Mass distribution of cellular components . . . . . . . . . . . . . . . .
18
1.2
Mass distribution of cellular components in model cell . . . . . . . . .
19
2.1
Yeast strains used in average and relative cell density measurements .
46
5.1
Density variation estimates for polystyrene beads . . . . . . . . . . .
93
5.2
Calibrations and cantilever geometry before and after KOH etch . . .
96
15
16
Chapter 1
Introduction
1.1
1.1.1
Background
Cell density fundamentals
Accurate measurements of cell size are fundamental to understanding the cell cycle
and to identifying cell type and cell state. During exponential growth, cells require
coordination between growth and division to maintain the population’s size distribution, but it remains unclear how cells monitor and regulate cell cycle entry in response
to cell size. The key to cell cycle control is the concentration of critical regulatory
proteins, which is defined not only by expression levels, but the volume of the cell.
Furthermore, cell volume is coupled to mass and energy requirements that control cell
division and survival. Changes to rates of mass and volume accumulation may be correlated with cell cycle position and can be measured as variations in cell density. Yet
even for model systems, such as the budding yeast Saccharomyces cerevisiae, these
cellular-level parameters remain poorly investigated mainly due to a lack of tools for
directly and accurately measuring cell mass or density.
A cell consists mainly of water and bulk protein (Table 1.1), and because each
have a relatively constant density, overall changes to the density of the cell represent
changes in the dry mass to water ratio. Table 1.2 details how water and dry mass each
can cause a 1% density increase (1.05 g/mL → 1.06 g/mL) in a 1000 fL cell. This density
17
Component
Water
Inorganic ions
Miscellaneous
small metabolites
Proteins
RNA
DNA
Phospholipids
Other lipids
Polysaccharides
Bacteria
Total Mass Dry Mass
70%
1%
3.5%
Animal cell
Total Mass Dry Mass
70%
1%
3%
3%
10%
3%
10%
15%
6%
1%
2%
2%
50%
20%
3.5%
6.5%
6.5%
18%
1.1%
0.25%
3%
2%
2%
60%
4%
1%
10%
6%
6%
Table 1.1: Approximate mass distribution of cellular components in bacteria
and animal cells. Water makes up the bulk of a cell’s mass no matter the cell
type, and soluble protein is the second largest component. The ratio of these two
components likely determine cell density. Table adapted from [3].
increase can result from either a ∼13% increase in the cell’s dry mass (+4% change
in cell volume), or if the density increase is caused by water changes alone, a ∼23%
decrease in the cell’s total volume. These changes affect cell volume differently, a fact
which may be used to predict the mechanism for any change in cell density. If both dry
mass and water are altered, the changes to these components may be less pronounced
and still cause a 1% density change. Also, if an increase in dry mass is concentrated
in a more specific macromolecule category, the required dry mass increase will be
proportionally larger. Another clue to a density change’s mechanism is timescale.
Large-scale protein and ribosomal synthesis occur over hours, but changes to cell
water content can occur in seconds, such as in response to osmotic shock.
1.1.2
Methods to measure cell size and density
Current methods for measuring cell density are limited to indirect measurements
and density gradients (Fig 1-1), which can yield conflicting results. The density of
fission yeast has been reported as cell cycle-dependent via interferometry [46] and cell
cycle-independent via density gradient centrifugation [40]. It is reported in [40] that
18
Density (g/mL)
Component
Water
Protein
Small Metabolites
Lipids
Other
Dry Mass (pg)
(Percent change)
Cell Volume (fL)
(Percent change)
1.05
Initial mass (pg)
735
189
32
50
44
315
1.06
Mass (pg) with ∆m
735
213
36
57
50
356(+13%)
1.06
Mass (pg) with ∆V
568
189
32
50
44
315 (0%)
1000
1041(+4%)
833 (-23%)
Table 1.2: Mass distribution of cellular components in model cell. Mass
contributions from major cellular components and how each change during a density
increase caused by changes to dry mass (∆m) or water (∆V) alone. For both types
of density increase, the volume of the additional components was assumed to be:
water∼1.0 g/mL, and other∼1.3 g/mL.
Figure 1-1: Sample density gradient following centriguation during which the sample
is separated by density into two distinct bands. Figure adapated from [10].
19
excessive sample manipulation may have influenced the interferometric results. Even
so, measurements in density gradients can be complicated by possible interactions
between the cells and the gradient medium [49, 39]. Density measured by gradient
centrifugation has been reported as cell cycle-independent during the Chinese hamster
ovary (CHO) [5] and murine cell cycles[42], either independent or dependent on the
E. coli cell cycle [39, 66, 53], and cell cycle-dependent for budding yeast [31, 6].
Density gradient centrifugation has major deficiencies in density measurement
applications:
(1) Not a single cell measurement. Density gradient centrifugation provides relative density averages for subpopulations separated on the same gradient. It
cannot measure the distribution of density within a population or identify rare
cells based on density.
(2) Difficult to repeat and calibrate. Gradient formation is highly dependent
on experimental conditions. In order to obtain absolute densities and compare
across gradients, especially with high resolution gradients, each gradient must
be calibrated. Calibration is performed by colored beads of known densities
or by measuring the refractive index of a gradient fraction. Density values are
interpolated between bead standards with limited density resolution and fractionation for refractive index measurements disturbs the gradient profile.
(3) There is a tradeoff between dynamic range and resolution. A high dynamic
range gradient necessitates steep changes in density because the gradient is a
finite length. Additionally, band position quantification has limited resolution,
and therefore a wide range gradient will have very limited resolution. The gradient must be designed with this range and resolution tradeoff in mind, which
often requires prior knowledge of the sample’s density and variation. Centrifugation conditions not only affect the gradient profile, but are also expected to
influence resolution: “Whether a gradient has sufficient resolving power to give
such a separation between zones of particles is dependent on (a) the mass of
the particles in each zone, (b) the homogeneity of the particles, (c) the nature
of any particle-solvent interactions, (d) the slope (dρ/dr) of the gradient, (e) the
20
speed of the rotor, and (f) the type of rotor used” [10].
(4) Long exposure to non-ideal environment. Most density gradient chemicals
(salt, sucrose, iodinated compounds) alter solution tonicity (see §5.7) and therefore cell volume, which directly affects cell density. Cells are exposed to these
gradient chemicals for the duration of the centrifugation (10-30 min), often at
low temperatures in order to reduce diffusion away from the band ([35]), and
this procedure affects the property being measured—density.
It is a common misconception that the width of the band resulting from centrifugation (such as those shown in Fig 1-1) directly correlates with density variation. In
fact, the width is more directly related to rotor speed as “a balance between spreading by diffusion and contraction under the influence of the centrifugal field” [35].
Many sources disturb the gradient and widen this band: rotor speed, deceleration of
the centrifuge, fractionation, and overloading of the gradient. Upon deceleration the
top and bottom of the gradient are disturbed. Fractionation for sample extraction
or calibration drags dense bands along the tube walls, allows for water evaporation,
temperature, and vibration disturbances. Finally, interactions between the gradient
material and the particles being measured affect band width, and the capacity (cell
concentration at which there is no gradient distortion) is often less than predicted
[10]. Despite these, density gradient centrifugation reports a 0.005 [35]-0.002 [10] g/mL
resolution, but today is mostly limted to fractionating and purifying a variety of cells
and subcellular components [10].
The ideal density measurement would directly monitor mass and volume of each
cell within a population with minimal sample perturbation and allow cells to be collected for subsequent measurements. Towards this aim, we utilized the suspended
microchannel resonator (SMR) to measure single cell buoyant mass with high precision and calculate cell density.
21
1.2
1.2.1
SMR description and measurements
Device concept and basic operation
Recent development of the suspended microchannel resonator (SMR) has enabled
novel label-free biological sensing applications with unprecedented mass resolution
(∼1 femtogram in a 1 Hz bandwidth) [16]. The SMR is a microfluidic device that improves mass resolution by putting liquid samples inside a vacuum-packaged cantilever
(Fig 1-2). A cantilever resonates at a frequency proportional to its total mass, and
as an individual cell travels through an embedded microchannel, the total cantilever
mass changes. This change in mass is detected as a change in the resonance frequency
that corresponds directly to the buoyant mass of the cell (1-2B).
The SMR’s unique vacuum-packaging reduces cantilever viscous damping and improves the cantilever’s frequency resolution, or quality factor. Quality factor is a
measure of resonator damping and may be estimated from an oscilloscope display of
bending position vs time as Q =
ωf/∆ω ,
where ωf is the cantilever’s resonance fre-
quency (maximum signal amplitude) and ∆ω is the frequency range over which the
signal amplitude decreases by 1/2.
In order to increase the amplitude of vibration at the SMR’s natural resonance
frequency, the cantilever is actuated electrostatically by an electrode patterned on the
bottom of the vacuum cavity and the cantilever’s conductive silicon. The resonance
frequency is detected by an optical lever system similar to an AFM. A schematic of
the electronic drive and detection system is given in Fig 1-3. Briefly, a focused laser
beam reflects off the top surface of the cantilever and its position is detected by a
split photodiode. As the cantilever vibrates in- and out-of-plane, the reflected laser’s
position scans each of the photodiode’s sensors and the resulting sinusoidal signal is
amplified by a photodetector board (schematic in [15]). The photodetector’s signal
is part of a feedback loop with the drive circuit, which outputs the electrostatic drive
signal for the SMR. The cantilever’s resonance frequency is recorded by a frequency
counter (HP 53131A, 2 Hz acquisition rate) and a data acquisition (DAQ) system.
Although the frequency counter can accurately detect the baseline signal, it is not
22
Figure 1-2: Illustration of instrument and cell measurement. (A) The cantilever vibrates in- and out-of-plane with an amplitude of a few hundred nanometers.
Cells flowing through the vibrating cantilever microchannel displace a volume of fluid
equal to their own volume and, at a given position, change the cantilever’s resonant frequency proportional to this change in cantilever mass. The flow rates are
controlled by pressure. The number of single cell measurements was maximized by
adjusting the sample concentration. A more detailed description of the instrument
and its operation is available in [16]. (B) The frequency shift as cells flow through
the microchannel (four of which are shown) changes with position because the cantilever’s angular velocity is position-dependent [19]. The maximum frequency shift
(red circles), which is proportional to the recorded buoyant mass, occurs when the
cell is at the cantilever tip. Since the recorded buoyant mass depends only on this
maximum frequency shift, the measurement is independent of the particle’s path up
until the cantilever tip. Further details about path variation at the cantilever tip are
provided in §5.8. The frequency returns to baseline upon each cell’s exit from the
cantilever.
23
Figure 1-3: Fluidic and Electronic Schematic of the SMR system. The SMR
is electrostatically driven by a feedback control system and the detected resonance
frequency is convolved with a synthetic sine wave (Function Generator) for high resolution frequency detection. Fluid is driven via pressure through the system using pressurized glass vials and pneumatic valves. Equipment identification: DAQ—
NI PCI-6259, frequency counter—HP 53131A, electronic regulator—Proportion Air
QPV1-TFEE-030-CXL (40 Pa resolution), pneumatic valve (X)—SMC S070C-6DG32, and manual (unlabeled) regulators—Omega PRG101-25.
24
suitable for the more rapid changes to cantilever resonance frequency observed with
cells (transit time 0.1-1s). The DAQ system, though faster, is limited by its onboard
counter (80 MHz) and cannot accurately measure the high frequency photodetector
output (fr >1.5 kHz). Thus, the signal is mixed down with a generated sine wave
via a multiplier board prior to acquisition (schematic in [15]). The multiplier board
convolves the photodetector output signal with the synthetic sine wave to produce
an output with a frequency that is the difference between its two input signals. If
the synthetic sine wave frequency is known, the cantilever resonance frequency may
be calculated from this mixed down signal. The multiplier board output frequency is
the DAQ system’s rate of acquisition and is user-set at >1kHz for accurate particle
buoyant mass measurements.
Sample delivery and fluid flow rates in the SMR system are all controlled via
pressure. A fluid schematic for a population-style buoyant mass measurement is
provided in Fig 1-3. During this measurement thousands of particles are delivered
to the SMR and each are measured once before being rinsed down the waste bypass
channel. Pressurized glass vials (VWR #80076-582) with microcentrifuge tube inserts
for reduced sample consumption force sample and waste fluid through microfluidic
tubing and device channels. The sample (cells) and waste bypass fluid (PBS) are
delivered via P2 and P1 regulator activation (P2 ∼ P1 ). Once loaded, the pneumatic
valve, marked as (X) on Fig 1-3, is actuated and the sample bypass channel is held
at constant, or “matched,” pressure. The electronic regulator, P3 , is then used to
control the direction and flow rate in the cantilever microchannel , which also controls
particle transit time. Although all pressure sources are similar in magnitude, one of
the waste bypass pressure sources (typically P3 ) must be less than P2 to ensure
cells flow through the SMR from the sample to waste bypass channel. Continuous
adjustments to P3 may be required during an experiment to maintain particle transit
time. Ultrafine adjustments to pressure may be produced via vial and fluid height,
which may also change the rate at which particles enter the cantilever microchannel
(see §5.6). Particle size biasing (see §5.6 and Fig 5-5) may be reduced by periodically
(every 1-4 minutes) switching the pneumatic valve and exhausting the downstream
25
sample bypass channel vial to rapidly flush fresh sample into the device.
1.2.2
Buoyant mass as a physical property to characterize
single cells
Buoyant mass, the effective mass of an object in fluid, is a balance between gravity
and buoyancy. In equation form, buoyant mass is:
mB = Vcell · (ρcell − ρf luid )
(1.1)
= mcell − Vcell · ρf luid ,
(1.2)
where mB is the buoyant mass of the cell, Vcell is the cell volume, ρcell and ρf luid are
the density of the cell and the fluid, respectively, and mcell is the absolute mass of
the cell. Buoyant mass for a given particle changes with fluid density and is positive
or negative depending on how the cell density compares to that of the surrounding
fluid. Details regarding how errors in buoyant mass data caused by variations in fluid
density between cell samples can be minimized are provided in §5.3.
Since most reported cell mass data are in terms of dry mass, it is important to
consider how buoyant mass relates to the dry mass of a cell. The basic equation for
buoyant mass (Eqn 1.2) may be divided into “dry” and “wet” components, which
correspond to the cell’s dry and water mass:
mB = mdry + mwet − Vcell · ρf luid .
In the special case where the fluid density is equal to that of the cytoplasmic fluid:
mB,cytoplasmicf luid = mdry + Vwet · ρcytoplasmicf luid − Vcell · ρcytoplasmicf luid
= mdry − Vdry · ρcytoplasmicf luid
= Vdry · (ρdry − ρcytoplasmicf luid ),
the result is not unlike Equation 1.1 and presents a method by which dry mass may be
26
estimated from buoyant mass given an average density of cellular components (ρdry :
proteins, lipids, nucleic acids in their respective proportions) and cytoplasmic fluid.
Of course, the cell need not be measured in cytoplasmic fluid directly and the fluid
density may be corrected to that of cytoplasmic fluid using an approach similar to
Eqn 5.2, but assumptions beyond the average dry mass density will introduce further
error. Despite these caveats, the ability to measure cellular buoyant mass presents
several novel methods to measure cell density and investigate how density changes as
a function of cell type, state, and response.
27
28
Chapter 2
Average and relative cell density
measurements with the SMR
Studies using density gradient centrifugation have suggested that the changing density of budding yeast may correlate with bud formation [40, 48] or cyclic changes in
water content and vacuole dynamics [6]. Although more than one factor likely contributes to cell cycle-dependent density variation (or lack thereof) across cell types,
mechanisms that give rise to density variation in budding yeast may be conserved in
other eukaryotes. We measured density in two ways with the SMR. The first provides
an alternative to density gradient centrifugation and population-based approaches
described previously [27] by measuring buoyant mass with the SMR and, on the same
sample, volume with a commercial Coulter counter. Unlike density gradient centrifugation, this technique provides buoyant mass and volume information, measures
growth-arrested cells in almost any medium, and does not require density gradient
chemicals. With this method we found that cell density increases prior to bud formation at the G1/S transition. To investigate the origin of this density increase, we
used the SMR in a second method where relative density changes of growing yeast
cells are measured as the cells are sampled by the microchannel. We found that
the density increase requires energy, passage through START, function of the protein synthesis regulator TOR, and an intact actin cytoskeleton. In conjunction with
these density measurements, FACS analysis and bud emergence data suggest that
29
this density change is independent of DNA replication and may result from several
START-dependent events.
2.1
Density, volume, and buoyant mass of growtharrested cells
Cell buoyant mass, volume, and density were measured by combining the SMR’s
buoyant mass readout with a commercial Coulter counter’s volume measurements.
Buoyant mass is the change in cantilever mass as a cell transits the channel, or
the difference between the mass of the cell and the mass of the displaced fluid. The
relationship between a cell’s buoyant mass and the fluid density is linear, and the slope
of this line is related to the cell volume (Fig. 2-1). Cell density can be extrapolated
from this line as the point at which buoyant mass is zero, or at which fluid density
exactly matches cell density. For populations, the flow-through configuration of the
SMR allows cells to be collected during the buoyant mass measurement (Fig 5-5)
and used in downstream measurements for paired data analysis, such as volume, but
this yields relatively few cells (n<3000). Volume measurements (n>20,000) recorded
before the sample was loaded in the SMR were used in the density calculation. In
this way buoyant mass and volume measurements are made with the same sample,
the data are pooled into buoyant mass and volume histograms and each histogram is
fit to a log-normal function. To calculate the density of a cell population, the means
of the fitted functions are substituted into:
ρ = ρf luid + mB /Vcell ,
(2.1)
where ρ is the cell density, ρf luid is the fluid density, mB is the buoyant mass, and
V is the cell volume. Details regarding fluid density determination are provided in
§5.2, and for comparisons between samples, the cell buoyant mass was adjusted for
the fluid density of water at 20◦ C (0.9982 g/mL) by Equation 5.2. This technique was
verified with 3.67±0.1 µm diameter NIST particle size standards. The beads have a
30
Figure 2-1: Cell density, mass, and volume measurements. Cell density is
calculated by the linear relationship between buoyant mass and fluid density (red
line, equation in text). The slope of this line is determined by the cell volume (inset
a) and is measured by a commercial Coulter counter on the same sample loaded in
the SMR. The buoyant mass (inset b) is determined by a distribution of >1500 SMR
measurements. An example of four of these measurements made in phosphate buffer
is in Fig. 1-2B. The means of the fitted log-normal functions (X on insets) are used
to calculate average cell density.
31
mean 1.38±0.010 pg buoyant mass in water (T∼20◦ C, fluid density = 0.9980 g/mL)
and a 27.0±0.10 µm3 mean volume. We calculated the density of the particles to be
1.0486±0.0010 g/mL, which is in accordance with the accepted polystyrene density of
1.05 g/mL. Error in the volume and mass parameters both contribute to this density
calculation. The Coulter counter’s error results from inherent instrument noise. The
SMR’s main source of error is peak height determination (details in §5.1) and variation
in particle position at the cantilever tip (details in §5.8). Position variation contributes
∼6% to the measurement’s uncertainty for a 3.67 µm diameter particle, slightly less
than the inherent size deviation of the population. This error decreases with increased
particle diameter and is generally not significant for populations with larger size
variation, such as cells. The SMR also has a relatively low throughput compared to the
Coulter counter. For NIST particle standards we recorded >300 SMR measurements
in <30min, and for cell samples we recorded >1500 SMR measurements in <1hr.
For both particle standards and cells, >20,000 Coulter counter measurements were
recorded in <1min.
2.1.1
Yeast density is coordinated with the cell cycle
The yeast cell cycle is a highly regulated series of events controlled by the activation of cyclin-dependent kinases (CDKs) by cyclins. CDK activation drives cell cycle
progression and it is suggested that the expression level of a certain cyclin, Cln3,
serves to coordinate size, mass and volume, with entry into the cell cycle [59]. The
point at which cells commit to cell cycle entry is called START or Restriction Point
[51]. To determine how cell density correlates with the cell cycle, we measured the
distributions of buoyant mass and volume in budding yeast populations. The density
of asynchronous budding yeast in our strain background, W303, was 1.1029±0.0026
g/mL
(Fig. 2-2A), slightly lower than the density of 1.1126 g/mL reported by density
gradient centrifugation in the Y55 strain [6]. Since cells are not uniformly distributed
through the cell cycle in an asynchronous population (∼80% of W303 cells are in Sor M-phase, estimated by budded cell counts), this density is expected to be weighted
by the time cells spend in each phase of the cell cycle. We next measured the buoyant
32
Figure 2-2: Density, buoyant mass, and volume of cells synchronized by cell
cycle blocks. (A) WT (A2587) and cdc28-as1 (A4370) densities (mean±SD)
in arrested G1 and metaphase are lower than asynchronous mock-treated (Untreated, DMSO) populations. The density of the asynchronous population is approximately the same as S-phase arrested cells and reflects the unequal distribution
of cells throughout the cell cycle. Cells were synchronized with alpha-factor (AF)
for 2h (5µM), 1-NM-PP1 (pp1) CDK inhibitor for 3h (5µM), hydroxyurea (HU)
for 2h (10mg/ml) and nocodazole (noc) for 2h (15 µg/mL), as indicated. Fixed
cells were fixed in 3.7% formaldehyde for various amounts of time. (B) Buoyant
mass (ρf = ρwater,20◦ C ) and volume measurements for the same cell populations
(mean±SD).
33
mass, density, and volume of cells arrested in various stages of the cell cycle. The density of cells arrested in G1 by treatment with the pheromone alpha-factor decreased
1.7% to 1.0846±0.0043 g/mL. The decrease in G1 density was also observed in cells
arrested using the analog-sensitive CDK mutant cdc28-as1. This allele responds to
the ATP analog 1-NM-PP1, which produces a G1 arrest by selectively occupying the
modified ATP binding pocket of Cdc28-as1 and inhibiting CDK activity [11]. Cells
arrested in G1 via cdc28 inactivation (pp1) had a density of 1.0812±0.0100 g/mL, a 2%
decrease from the 1.1034±0.0022 g/mL density of asynchronous cdc28-as1 populations.
Despite the longer arrest, 3h, and larger cell volume (Fig. 2-2B), arrested cdc28-as1
cells had a density similar to that of a 2h alpha-factor arrest, which may indicate wellmatched mass and volume growth rates between these G1 arrests. The density of cells
arrested in S-phase by the replication inhibitor hydroxyurea (HU) was 1.1049±0.0024
g/mL,
approximately the same as the asynchronous population. S-phase arrested cells
could be expected to have a higher density based on previous findings [31, 6], and
our result may be an effect of the drug or indicate differences between S-phase arrested cells and those in an asynchronous population. The density of cells arrested
in metaphase by the microtubule inhibitor nocodazole (noc) was 1.0998±0.0049 g/mL,
or ∼1.5% decrease from the mock-treated (DMSO) asynchronous culture density of
1.1173±0.0176 g/mL. These results suggest that density for arrested populations is cell
cycle-dependent, which further supports the findings by others [31, 6] that density is
regulated by cell cycle progression.
Since the differences in density could be artifacts of the different treatments or the
cell cycle arrests, we sought to determine if cell density varied during an unperturbed
cell cycle. For this purpose we measured the buoyant mass, volume, and density of G1
cells isolated by centrifugal elutriation, resuspended in medium for synchronous cell
cycle progression, and formaldehyde-fixed overnight. Although fixation artificially
increases cell density (Fig. 2-2A), the relative density throughout the timecourse
(Fig. 2-3A) agrees with our previous observations and others’ [31, 6]. Cell density
was correlated with cell cycle position by comparing the cell density with the percent
of budded cells (Fig. 2-3A, numbers in brackets). The density is relatively low in
34
Figure 2-3: Density, buoyant mass, and volume of cells synchronized by
elutriation. (A) Density of formaldehyde-fixed cell populations (A11311) grown
overnight in YEP + 2% raffinose and a synchronized sample was selected by centrifugal elutriation. Bud counts are reported as percent budded in brackets next to each
measurement. Cells begin to enter S-phase between 60 and 120 min. Error bars are
the SEM measured with a single fixed sample of elutriated wild type cells (A11311,
n=3). (B) Buoyant mass (ρf = ρwater,20◦ C ) and volume increase throughout the timecourse. Changes in cell density at the population level are the result of differences in
the relative rates of mass and volume increase through the cell cycle.
35
elutriated G1 (unbudded) cells, increases to near maximum during late G1 and Sphase entry (bud formation), and then decreases through mitosis. The recorded cell
density does not return to its minimum at the end of the first cell cycle because of the
timecourse’s resolution, loss of synchrony, or a possible elutriation effect on the initial
selection. Buoyant mass and volume continue to increase throughout the timecourse
as the cells grow and the population adjusts from the elutriation’s size selection (Fig
2-3B).
2.2
Continuous buoyant mass and volume measurements of synchronized cells
Although the density of arrested cells can be calculated with high precision because
buoyant mass and volume are measured over an extended period, this limits the
temporal resolution and makes it difficult to observe growth dynamics. In order to
address this limitation and to measure an uninterrupted cell cycle, we continuously
sampled from split cultures of elutriated G1 yeast cells that remained in medium
for both measurements. Cells measured by the Coulter counter were maintained in
an unshaken flask at room temperature and a small fraction was measured every 10
minutes and discarded. Cells measured by the SMR were maintained in an unshaken
vial at room temperature and freshly drawn into the system every 2 minutes and then
discarded, so no single cell spends more than 2 minutes in the system and there is little
opportunity for stress imposed by the microfluidic system to affect the cells’ buoyant
mass. Buoyant mass and volume growth rates increase during the cell cycle and the
coefficient of variation for volume is greater than that observed in buoyant mass (Fig
2-4, Fig A-2–A-4). The distributions widen as the culture loses synchrony and cell
size variation emerges. Although the smaller sample size prevented accurate density
calculations, this approach offers a powerful means to observe growth dynamics in
synchronized cell populations.
In summary, our data show budding yeast increase volume and buoyant mass
36
Figure 2-4: Buoyant mass and volume growth rates are cell cycle-dependent.
Color designates the fraction of the population with the indicated buoyant mass and
volume (color bar at right). Small unbudded cells (A2587) were isolated by elutriation
for synchronous culture after overnight growth in YEPD, which partially reduced
synchrony. (A) The SMR steadily sampled from the culture and measurements were
broken into 10 minute divisions (N=7839 cells). (B) Volume measurements on a split
culture were made from aliquots drawn at 10 minute intervals and recorded in <1min
(N=67607 cells). Additional budding data are available in Fig. A-1.
growth rates through the cell cycle, undergo periodic oscillations in cell density, and
a density increase begins before bud formation, which may result from several STARTdependent events. To test these we next developed a technique to observe cell density
changes in real-time, which is not possible with our previous methods.
37
Figure 2-5: Real-time relative cell density measurement. Cell state, distinguished by
cell density, is determined by the cell’s direction of frequency shift in a medium with a
density slightly above that of G1 cells. G1-synchronized cells have a negative buoyant
mass (positive frequency shift), and cells entering S-phase at a later timepoint have
a positive buoyant mass (negative frequency shift). The proportion of cells in each
state is directly correlated to the percent of cells below or above fluid density and
changes as cells synchronously progress through the cell cycle.
2.3
Single-cell relative density measurements in Percoll medium
The SMR reads out real-time changes in relative cell density via the direction of
change in buoyant mass as synchronized and growing cells flow through the cantilever.
A cell with a density greater than that of the fluid appears as a positive buoyant mass,
and a cell with a density less than that of the fluid appears as a negative buoyant mass
(Fig 2-5). If the medium density is adjusted to be between the initial and final cell
densities, then the ratio of the positive to total number of measurements in a short
time (1 min) approximates the fraction of cells in the higher density state at that
time. This single-cell technique enables the timing and detection of density changes
in biological samples as they occur in growth medium. It has higher time resolution
than current gradient-based approaches and does not involve a subsequent gradient
fractionation to define the density distribution [66]. This method may also be applied
to cells transitioning to lower density by decreasing the fluid density to below that of
the cells’ initial density.
The precision of SMR density measurements described in §2.3 rely on the method
for modifying the fluid density, the SMR’s resolution, and the degree of overlap in the
38
density distributions of the two cell states. To modify the density of yeast medium
(YEPD) we selected Percoll (Sigma-Aldrich), a colloidal silica suspension, for its low
osmolality, low viscosity, and general impermeability of biological membranes [1]. Experiments with Histodenz (Sigma-Aldrich) showed density changes for arrested yeast,
likely through an osmotic response, such as is observed in bacteria [7]. The resolution
of the 8 µm tall SMR used for these experiments is ∼3 fg (1 Hz bandwidth). This
can detect a 0.1% yeast density change in a high-density solution and we measured
∼2% change through the cell cycle. By measuring trends in synchronized populations,
sample number increases and the method’s statistical precision and reproducibility
further improves.
2.3.1
The G1/S density change in yeast
We used this method to further investigate cell density changes in yeast and how
density is coupled to the G1/S transition. Changes in density are indicative of differences between rates of total mass and volume increase, which may be correlated
to specific cell cycle events. Cells were first synchronized via alpha-factor, released
into a YEPD:Percoll medium (fluid density∼1.086 g/mL), and as the cells progressed
through the cell cycle they were continuously flowed through the SMR for singlecell buoyant mass measurements over a timecourse. As cells neared S-phase entry
and became denser, the proportion of cells with a density above that of the fluid
increased (Fig. 2-6, Mock-treated release). This shift demonstrates that alpha-factor
treatment arrests cells before the density increase observed in the unperturbed cell
cycle of G1 elutriated cells. It is consistently observed following alpha-factor release,
but the kinetics are not always identical. The timing and rate of this density shift
depends on the cell treatment, efficiency of release, and the difference between cell
and medium density. If the difference between the cell and medium densities varies
between experiments, then the timing of the density change, the point at which the
cell density is greater than that of the medium, will also vary. These variances are
responsible for the differences in mock-treated WT behavior observed during the experiments of Fig. 2-6. Although the technique is not suitable for quantifying density,
39
Figure 2-6: Changes in cell density require energy, TOR function, passage
through START, and an intact cytoskeleton.WT cells (A2587) were arrested
in alpha-factor and released in YEPD:Percoll medium with each treatment. Increases
in the percent of cells with a density above that of the fluid signify an overall increase
in cell density. Rapid fluctuations in these data are not expected to be biologically
relevant, but instead stem from measurement error, including slight fluctuations in
fluid density. (A) Azide (0.1% w/v) prevented the density change and demonstrates
an energy requirement for the density increase. Mock-treatment: equal volume water. (B) Rapamycin (10µM) prevented the density change and establishes a TOR
function requirement. Mock-treatment: equal volume 70% ethanol. (C) Alpha-factor
(5µM) prevented the density change and confirms a passage through START requirement. Mock-treatment: equal volume DMSO. (D) LatA (100µM) prevented the
density change and establishes a requirement for an intact actin cytoskeleton. Mocktreatment: equal volume DMSO. Error bars are the standard error of the proportion.
The Bonferonni-corrected significance for each treatment was p∼0.01 for (A), p∼0.05
for (B), p∼0.04 for (C), and p∼0.06 for (D).
40
it does enable the real-time detection of relative density changes that occur near the
medium density and, by the rate of transition, provides some information regarding
population synchrony.
2.3.2
The change in yeast density at G1/S requires energy,
TOR function, passage through START, and an intact
cytoskeleton
To characterize the yeast density shift at the G1/S transition as an energy-dependent
process we blocked ATP synthesis with sodium azide, an inhibitor of F1-ATPase,
immediately following release from an alpha-factor arrest. The SMR’s buoyant mass
measurements detected a cell density change in mock-treated control cells and no
change in density for cells treated with azide (Fig. 2-6A). Thus, the density change
we previously observed is an active process requiring ATP.
The TOR pathway controls translation initiation and stimulates protein synthesis
in response to nutrients [18]. To examine whether the density shift depends on protein
synthesis, we asked whether the TOR pathway was required. We treated cells released
from an alpha-factor-induced arrest with rapamycin, an inhibitor of TORC1 function
[33], and compared the percent of cells with a change in density to the resulting
percentages for a parallel-grown mock-treated control culture. Cells from the control
culture changed in density and cells with TOR inactivation did not change in density
(Fig. 2-6B). Thus, the change requires TOR function and likely, protein synthesis.
To determine whether START is required for the density change, we prolonged
a G1 arrest via continuous treatment with alpha-factor. Mock-treated cells released
into fresh YEPD changed in density and cells which were resuspended in alpha-factorcontaining medium displayed no significant change in density during an 85 min timecourse (Fig. 2-6C). These results suggest that the density shift is START-dependent,
but does not indicate whether it results from bud formation, DNA replication, or
some other START-dependent process.
Bud formation requires polarization of the actin cytoskeleton, and we investigated
41
the possibility that the actin cytoskeleton has a function in the cell density increase.
We treated cells released from an alpha-factor arrest with an inhibitor of actin polymerization, latrunculin A (LatA). We measured a change in density for mock-treated
control cells and no change in density following LatA treatment (Fig. 2-6D). We also
monitored bud appearance for similarly treated cells and confirmed that the LatA
treatment severely inhibited bud formation (Fig. A-5A). Thus, disruption to the
actin cytoskeleton prevents the density change, which may be the direct effect of perturbing actin-dependent processes such as vesicular transport required for growth, or
result from other LatA effects on cell growth [38].
To investigate if the density change also requires DNA replication, we examined
DNA content by FACS analysis. Cellular DNA was fluorescently labeled and the
distribution of relative DNA content (Fig. 2-1C) was measured for synchronized
samples. The LatA and rapamycin treatments following release from an alpha-factor
arrest reduced DNA replication by nearly the same amount (Fig. A-5B). At 60
min, ∼10% of the mock-treated and ∼35% of the LatA- and rapamycin-treated cells
exhibited 1C DNA, or had not yet replicated (Fig. A-5C). The rapamycin treatment
following release from an alpha-factor arrest also severely inhibited bud formation
(Fig. A-5A). Rapamycin is known to prevent entry into the cell cycle by inhibiting
translation initiation [18]; however, we have observed the effects of rapamycin to
be more severe on budding than on replication. Rapamycin- and LatA-treated cells
do not change in density and do not form buds, but do replicate to a significant
extent. Therefore, the change in density near the G1/S transition is independent of
DNA replication, and inactivation of actin-related processes, such as cell polarization,
budding, and/or vesicular transport may inhibit pathways required for this density
change.
Understanding the mechanism for this cell cycle-dependent density change is important in describing cell growth dynamics. A density change confirms that changes
to total mass (protein synthesis, vacuolar dynamics) and volume increase (membrane
growth) are not directly proportional, and the requirements for a density change at
the G1/S transition of budding yeast demonstrate a coupling between these two pro42
cesses. We have observed that perturbations to membrane growth early in the cell
cycle, such as the inhibition by LatA of budding and growth, abolish changes in density, and previous studies have shown that protein synthesis is linked to membrane
growth [47]. A change in density, or differences between mass and volume rates of
increase, may occur as a result of a transient increase to mass accumulation during polarized membrane growth at the G1/S transition, a slowdown in membrane expansion
during coordination with bud formation, and/or changes to cell water content, such as
by changes to vacuole size. If vacuole size is cell cycle dependent, then it would serve
as a clear explanation for the cell cycle dependent density change observed in yeast,
but without this knowledge, it remains a strong possibility that the cell’s preparation
for bud formation and the duplication of cellular machinery cause an increase in cell
density that is countered once the bud forms and cell volume increases. One caveat
in this hypothesis is that pheromone-treated cells, while polarized, remain low in
density. However, this may result from decreased protein synthesis and other effects
of alpha-factor treatment [29]. In regards to vacuole size and its influence on cell
density, Cln3 regulates vacuole size at the G1/S transition [30] and cells with larger
vacuoles have decreased density [31]. We have measured vps33∆ mutants (small,
fragmented vacuoles) in the S288C background to have a density ∼0.8% greater than
the wild type density of 1.1174±0.0039 g/mL, as in [48]. Analysis of the vacuole’s role
in cell cycle-dependent density changes is complicated by long cell cycle times in class
I vacuole mutants and thus little is known about how the vacuole affects cell density
at the single cell level and during a normal cell cycle.
2.4
Conclusions and Future Directions
We have presented mass, density, and volume measurements throughout the cell cycle and applied two new measurement techniques to identify the density change in
budding yeast at the G1/S transition as dependent on energy, TOR function, passage through START, and the actin cytoskeleton. One possible model for the density
43
variation with these dependencies is one in which polarized growth enables processes
during late G1 to increase cell density and changes in volume during bud formation
at S-phase decrease cell density. This linkage between mass and membrane growth is
central to how the cell coordinates growth with division and may have an important
role in the signal for cell cycle progression. The density measurement techniques may
be generalized to other cells and subcellular particles, and Chapters 3 and 4 describe
device developments that acquire single cell mass and density measurements at once
and with only the SMR. This, combined with the ability to continuously monitor
single cells, could detail the cell-to-cell variations that are otherwise obscured in population measurements and would provide the basis for a more complete understanding
of cell growth, division, and response.
2.5
Materials and Methods
SMR Measurements. Devices and fluidic controls are as described in [16] with the
exception of a larger (∼8x8 µm) cantilever channel cross-sectional area. Devices were
further enlarged to 9x9 µm by a KOH etch at 40◦ C post-fabrication (more details
provided in §5.5). Cell volume was measured twice for the density measurement in
the first method—once before the mass measurement and once on the sample of cells
collected from the SMR waste channel—to pair the measurements and ensure that
the measured cells were representative of the original sample.
Strains, growth conditions and sample preparation. Cells were grown in
YEP supplemented with 2% glucose (YEPD) at room temperature (21◦ C). Cells were
synchronized with 5 µg/mL alpha-factor at 0 and 90 min, for a total arrest of 120 min,
with the exception of cells synchronized by the 120 min hydroxyurea (10mg/ml) or
nocodazole (15 µg/mL) treatment. An equal volume DMSO mock-treated culture was
a control for the nocodazole measurements. For cdc28-as1, cells were arrested with
1-NM-PP1 (5 µM) for 3h. For the density measurements on growth-arrested cells,
cells were washed via vacuum filtration at 120 min and concentrated in phosphate
44
buffer to ∼108 cells/mL. Volume was measured on a Multisizer 3 Coulter counter fitted with a 100 µm aperture tube, the sample was delivered to the SMR, and the cells
were collected from the waste side of the SMR to be measured again with the Coulter
counter. We observed no change in cell volume resulting from suspension in phosphate buffer. We compared the original sample volume distribution to that of cells
collected from the SMR waste and directly observed the SMR’s preferential selection
of small particles. This bias was mitigated with higher flow rates. For real-time sample preparation, cells were grown and arrested as described above. Cells were washed
via vacuum filtration and concentrated in a 65:25:10 Percoll (Sigma-Aldrich, St Louis,
MO):4xYEPD:H2O solution to ∼107 cells/mL. Depending on treatment, alpha-factor
(5 µg/mL), azide (0.1% w/v), rapamycin (10 µM), LatA (100µM), DMSO, or ethanol
control was added to the cell suspension. Cell volume was recorded by a Coulter
counter and the sample was delivered to the SMR at room temperature.
Elutriation. Cells were grown overnight in YEP + 2% raffinose for density measurements (Fig 2-3) and YEPD for continuous measurements (Fig 2-6), synchronized
by centrifugal elutriation [4], and resuspended in YEPD. For continuous measurements the sample was concentrated and delivered to the SMR for mass measurement
in medium. Aliquots for fixed-cell density measurements were collected into 3.7%
formaldehyde at indicated timepoints. Fixation was required for a complete cell cycle
timecourse because the time required for the density measurement is much longer
than the cell cycle. Following fixation, cells were washed, resuspended in phosphate
buffer, the volume distribution was recorded on the Coulter counter, and the sample
was delivered to the SMR for mass measurement.
Flow Cytometric Analysis. Cells released from alpha-factor arrest were concentrated to ∼108 cells/mL in a 1 mL volume and shaken in an angled test tube at
275 RPM. LatA (100µM), rapamycin (10 µM), DMSO, or ethanol control was added
to each culture and 15 min timepoints were collected into 70% ethanol for 120 min.
Samples were prepared and stained with propidium iodide as previously described
45
Strain
A2587∗
A4370∗
A11311∗
BY4741∗∗
Knockout (KO) collection**
Relevant genotype
(WT) MATa, ade2-1, leu2-3, ura3,
trp1-1, his3-11,15, can1-100, GAL, psi+
MATa, cdc28-as1
MATa, ade1::HIS3, lys2::KanMX
(WT) MATa, his3D1, leu2D0, met15D0, ura3D0
MATa, vps33∆::KanMX
Table 2.1: Yeast strains used in this study
∗
strains in the W303 background
∗∗
strains in the S288C background
[36].
Statistical analysis. Slopes for each of the real-time density experiments were
calculated by linear regression. A 1-way ANOVA test was performed on the slopes
for the five groups (release from an alpha-factor arrest, azide, continuous alpha-factor
treatment, rapamycin, LatA), each with n=3. The release group consists of a control
measurement for the azide, rapamycin, and LatA treatments. A Bonferonni-corrected
t-test for the individual treatments and the release group was used to report significance of each treatment (Fig. 2-6).
46
Chapter 3
Single-cell density measurements
with a dual SMR
The SMR measures particle buoyant mass, a parameter that is dependent on the
surrounding fluid density (see §1.2.2), but which may be used to determine particle
density. Chapter 2 describes how to measure average particle density using a population’s buoyant mass and volume distribution to calculate the mean density of a
particle population. This approach is illustrated geometrically in Fig 2-1, in which
a point and slope define the average linear relationship between buoyant mass and
fluid density for a cell population. Godin, et al (Figure 2 of Ref [27]) used a twopoint approach in which particle populations were measured in fluids of two different
densities to calculate the average linear relationship and thus average density of a
population. In this chapter we describe a modified SMR device that utilizes the twopoint method (Fig 3-1A) to measure the mass, density, and volume of each particle
that passes through the system. We use this device to measure the variation in density
of cells and beads and to identify subpopulations by their mass-density signature.
3.1
Dual SMR concept and design
In order to measure a single particle in two different fluids, we developed the dual
SMR (Fig 3-2), which is similar to the system described in §1.2.1 and previously [16],
47
Figure 3-1: (A) Principle to measure single cell mass, volume, and density. By
weighing a cell in two fluids of different density and plotting the linear relationship
between buoyant mass and fluid density, the absolute mass (y-intercept), volume
(slope), and density (x-intercept) of the cell can be determined. (B) Frequency
change (directly related to buoyant mass) as a function of fluid density for melamine
beads. The variations in mass, density, and volume may be directly observed from
the intercepts and slopes created by each pair of buoyant mass measurements.
but with two fluidically connected and simultaneously operated cantilevers. A single
particle’s buoyant mass is measured in one cantilever (SMR1 ), then the particle exits
and continues down a microchannel connected to a T-junction, which introduces a
fluid of different density. After the T-junction, the particle continues through a long
serpentine channel to facilitate fluid mixing and finally enters a second cantilever
(SMR2 ) for a buoyant mass measurement in the mixed fluid of different density.
Since the same particle is measured in two different fluid densities, there are two
equations (Eqn 1.1 for each measurement) and two unknowns (Vcell and ρcell ). These
equations may be subtracted to calculate the cell’s volume:
mB,1 = Vcell · (ρcell − ρf luid,1 )
−
mB,2 = Vcell · (ρcell − ρf luid,2 )
∆mB = Vcell · (∆ρf luid )
∴ Vcell = ∆mB /∆ρf luid
48
(3.1)
Figure 3-2: Illustration of dual SMR instrument (A) Single particle mass and
density measurements with the SMR require a particle to be measured in two different
fluid densities. For the first measurement, particles enter from the large sample
bypass channel and flow through the first cantilever microchannel. The particle then
continues to a T-junction where a different density fluid (Fluid 2) is added and mixed
via diffusion along the serpentine channel. The second measurement is recorded as
the particle flows through the downstream SMR in the mixed fluid. (B) A dark
field image of second generation dual SMR devices. The two cantilevers are slightly
different geometries and a short serpentine channel at the Fluid 2 entrance enables
closer matched fluidic resistance at the T-junction.
49
Once Vcell is known, Eqn 1.1 may be used for either of the fluid densities to calculate
the cell density. Details regarding fluid density determination are provided in §5.2.
During testing of the dual SMR devices there were two unexpected results: (1)
baseline instability due to incomplete fluid mixing (see §3.1.1) and (2) cantilever
crosstalk (see §3.1.2).
3.1.1
Fluidic mixing in microchannels
Mixing in the dual SMR is limited to pure diffusion. Taylor dispersion, an enhanced
diffusion that can occur in laminar flow, is not observed in this channel geometry
because Taylor dispersion only acts to diffuse along a channel length [62]. In the dual
SMR, diffusion-based mixing occurs once the cell passes the microfluidic T-junction
(Fig 3-3), where high density fluid is added to the sample stream and the cell is
pushed to the opposite side of the channel in its original fluid. If the two fluids do not
Figure 3-3: A cell exiting the first cantilever passes by a T-junction, at which point
high density fluid is added to the stream. The two fluids mix across the channel
by diffusion and no mixing occurs along the channel length. The position of the
separating streamline (dashed line) is dictated by pressures and represents the ratio
of the two fluids.
mix, then the SMR2 buoyant mass measurement remains as that of a cell in medium,
but the assigned fluid baseline will be a ratio of the two fluids. In this case, or in
one of only partial mixing, the fluid density is overestimated and the particle volume
(slope on Fig 3-1) is severely underestimated. If the second fluid is lower in density,
then the error occurs in the opposite direction.
In order to estimate the time required for sufficient mixing, a simple 1D version
50
of Fick’s law of diffusion is solved:
c
· 100% = erfc
c0
w
√
2 Dt
,
(3.2)
where the left hand side is the percent progress to steady state, erfc is the error
function, w is the channel width, D is the diffusivity constant, and t is the time for
diffusion, the lag time, in the dual SMR. The results of this equation for different
channel widths and diffusion times are in Fig 3-4.
Figure 3-4: Diffusion-based fluid mixing as a function of time and channel width.
Degree of mixing calculated using Eqn 3.2, where D is that for Cs+ and Cl− ions in
water (∼1.24 x 10−5 cm2/s). The diffusivity constant for ethanol in water is ∼2.032 x
10−5 cm2/s. The diffusivity constant is not available for Percoll, but is expected to be
much less than that observed for ions in water.
Another estimator of the time required for diffusional mixing is the Peclet number,
a ratio of convection to diffusion:
Pe =
U0 w
,
D
(3.3)
where U0 is the average channel velocity, w is the channel width, and D is the diffusivity constant. Peclet number estimates the number of channel widths required for
complete mixing, which in consideration with the increased flow velocity following
the T-junction, is important in designing the mixing channel. The serpentine channel
51
length in the devices used for this work is 1.17 cm. The average lag time for an experiment is ∼5s (mean flow velocity∼250
µm/s),
which means that the mixing is ∼89%
complete for a 15x20µm device (Fig 3-4) and the Peclet number is ∼3. Complete
mixing in terms of the Peclet number refers to a characteristic diffusion length, which
is much less than the near complete steady-state mixing required by the dual SMR
system.
As a result of incomplete mixing, there is some baseline instability in the second
cantilever (SMR2 ). The stability depends solely on the fluid density, to which the
15x20µm SMR is sensitive at the rate of ∼1 x 10−5 g/mL per 1 Hertz frequency change.
This change corresponds to a <0.01% change in the fluid ratio between the two fluids
at the dual SMR’s T-junction. A stable baseline is easily achieved with a wellmixed, bulk fluid, but this is almost never true for the SMR downstream of the fluid
mixing T-junction (SMR2 , Fig 3-5A). Changes to the fluid ratio occur in the dual
Figure 3-5: Sample baseline instabilities in the second cantilever of the dual
SMR. (A) Baseline instability in SMR2 during cell measurements (cells indicated
by red X). (B) Example of peak shape when pressure fluctuations due to particle
entrance change the fluid ratio at the microchannel T-junction.
SMR as a result of pressure fluctuations and the diffusion of contaminating fluid
from dead volumes. One source of pressure fluctuations is instability in the pressure
regulators, which may be dampened with an upstream pressure reservoir (Fig 3-7,
1L glass bottle) and amplified by trapped air bubbles. Another source of pressure
fluctuations is caused by changes to the channel’s resistance when a particle enters
the cantilever microchannel. This is observed as a fluctuation in the fluid ratio in
front of the particle and as a baseline instability on the left hand side of the resonance
52
frequency shift in SMR2 (Fig 3-5B). If the channel size is increased relative to the
particle size, then this effect is decreased.
3.1.2
Cantilever crosstalk
Additional noise is detected in some cantilevers if the resonance frequencies of the two
dual SMR cantilevers are too similar (Fig 3-6A). The amplitude of this crosstalk noise
Figure 3-6: Frequency trace and theoretical frequency response for two
15x20 µm cantilevers. (A) Two frequency traces for a fluid-filled cantilever in
which the second on-chip cantilever has additional noise due to crosstalk. An overlaid
beat frequency is the difference in frequencies between the two cantilevers. The
amplitude of this beat frequency, or noise, increases as the cantilevers’ resonance
frequencies increase in similarity. (B) Theoretical resonance frequency response (Eqn
3.4) for two 15x20 µm cantilevers. Quality factor (∼3000) and resonance frequencies
(f1,water ∼239800 Hz, f2,water ∼242100 Hz) are as measured on a dual SMR. The degree
of crosstalk between the two cantilevers may be estimated from this calculation and
used in cantilever design and post-fabrication modifications.
increases with increased similarity between the two cantilever resonance frequencies.
Although it is always present, crosstalk can be effectively eliminated by significantly
altering the resonance freqeuncy of one cantilever, either by filling one with a fluid
of very different density, selectively etching one cantilever post-fabrication (see §5.5),
or designing the cantilevers to be different geometries. In order to predict the frequency difference required for minimal crosstalk, cantilever frequency response may
53
be calculated by:
#−1/2
" 2 2
2
ω
ω
Qm
,
Q2 1 − 2 + 2
H=
k
ω0
ω0
(3.4)
where Q is the quality factor, m is the cantilever mass, k is the stiffness, and ω0 is
the cantilever resonance frequency. An example frequency response for a 15x20µm
dual SMR is illustrated in Fig 3-6B, for which the magnitude of the interfering cantilever’s frequency response is compared to the resonance frequency (maximum) of
the cantilever of interest.
3.2
Dual SMR operation and fluidic control
Dual SMR actuation and resonance frequency detection are as described in §1.2.1,
with the exception of being in duplicate. Dual SMR fluidic control, however, is more
complex than single cantilever devices. Sample delivery and fluid flow rates are all
controlled via pressure. A fluid schematic for a population-style mass, volume, and
density measurement is provided in Fig 3-7. During this measurement hundreds
Figure 3-7: Fluidic schematic for a dual SMR. Fluid is driven via pressure
through the system using pressurized glass vials and pneumatic valves. The pressure
reservoir (1L bottle) dampens pressure fluctuations in the system. Regulators and
valve parts are as indicated in the caption of Fig 1-3. (Not shown) A polarized
beamsplitter enables a single laser to detect each cantilever’s resonance frequency
and electronics are duplicated as illustrated in Fig 1-3.
54
of particles are delivered to the SMR and each are measured in two different fluids
before being rinsed down the waste bypass channel. Pressurized glass vials force fluids
through microfluidic tubing and the device channels. The pressure reservoir dampens
pressure fluctuations in the system that would alter the fluid ratio at the T-junction
and result in SMR2 baseline instability. Tubing on either side of the high density
fluid channel’s bypass comes from a single pressure source, but are different inner
diameters to induce flow. At the start of an experiment, Fluid 2 is delivered via P3
regulator activation and allowed to fill both SMR1 and SMR2 until a steady baseline
is reached (up to 5 minutes for high viscosity fluids). Once loaded, P2 is activated for
cell delivery to the sample bypass channel, which is confirmed visually because the
P3 pressure is too high for the cell sample to enter the SMR microchannel. Once the
cells are loaded, P1 is activated and the pneumatic valve, marked as (X) on Fig 3-7,
is actuated such that the sample bypass is held at constant, or “matched,” pressure.
P3 is then slowly decreased until particles are observed in SMR1 . Adjustments to P1
may be necessary to control particle transit times in SMR2 , but these changes will
also affect SMR1 flow rates. Further fine adjustments to pressure may be controlled
via vial and fluid height. Changes to the sample fluid height will also change the rate
at which particles enter the cantilever microchannel (see §5.6). For consistent results,
care must be taken to maintain fluid heights during and between experiments. A
regular flush cycle in which the valve is switched to exhaust the downstream sample
bypass vial and P1 is turned off is implemented every 3 minutes for ∼30 seconds to
reduce particle size biasing and introduce fresh cells to the vicinity of SMR1 .
3.3
Data processing: Measurement concept and
peak pairing
Calculation of particle properties from the dual SMR requires the pairing of peaks
between two simultaneously collected frequency datasets. These datasets each have
hundreds (sometimes thousands) of peaks that correlate to a particle measured first
55
by SMR1 and then, at a later time (the lag time, Fig. 3-8A), measured by SMR2 .
The lag time is rarely constant throughout the measurement and there is never the
same number of peaks in each dataset. The lag time is directly correlated to the
fluid flow rate and small fluctuations in pressure can alter this time by 1-2 s (average
lag time ∼4-5 s). Datasets may have a different number of measurements because
particles may pass through the first cantilever and not the second if they stick in the
serpentine channel or flow into the high density fluid channel during a rinsing step.
Also, particles may pass through the second cantilever and not the first by unsticking
from the serpentine channel at a much later time or traveling as contaminants from
the high density fluid channel. These complications make it such that a simple time
offset between the two SMR datasets is insufficient to successfully assign peak pairs.
Dynamic programming recursively scores solutions to subproblems in order to find
an optimal solution to a larger problem [17]. The Needleman-Wunsch algorithm is a
dynamic programming method for DNA sequence alignment that optimizes alignment
by maximizing the number of perfect base matches and minimizing the number of
gaps in an aligned sequence. It is often used to locate a DNA sequence within an
organism genome and we present an adaptation in which it is used to align peaks
from the dual SMR’s datasets. The algorithm determines optimal alignment by first
calculating a matrix in which every possible base pair alignment is scored (Fig. 38B). The matrix recursively scores each base pairing using the upper, upper left,
and left neighboring value. The pair is assigned the highest score calculated from its
neighbors (base matches offer high positive scores, gaps (no match) and mismatches
offer lower scores). This recursive scoring enables the algorithm to consider new
gaps more detrimental than lengthening an existing gap. Once the matrix is created,
the optimized solution is calculated by starting in the lower right corner and finding
the most positive score of the same nearest neighbors used to create the matrix. A
diagonal move indicates a match and any other move introduces a gap. Although the
end result is the optimized solution, the algorithm has essentially scored all possible
alignments (including those with suboptimal, or mistaken, pairings) and discarded
these based on their low score.
56
Figure 3-8: Comparison between dual SMR peak pairing and NeedlemanWunsch algorithm. (A) Datasets from each cantilever are collected simultaneously
(top). The peaks in each dataset are located and the time at which the peak occurs
is recorded. A matrix records the calculated lag time for all possible peak pairs
(bottom). The optimal alignment is calculated by beginning at the lower right side
of the matrix and finding the lag time that best matches a user-initialized, predicted
value (0.5 for this example) in the upper, upper left, or left neighboring values. (B)
The two DNA seqeunces are obtained (top) and a scoring matrix is formed (bottom).
The scoring matrix calculates the score between all possible base alignments and the
optimal alignment is calculated similar to the procedure described in (A), except now
finding the most positive score.
57
In the dual SMR, peak pairs may be determined by a scoring matrix of lag times
(Fig. 3-8A). Pairs are made by starting at the lower righthand corner of the matrix
and moving to the upper, upper left, or left neighboring value that is most similar to
a user-initialized, predicted lag time. This user-initialized lag time is determined by a
short script, which finds the lag time that produces the most number of peak pairs, or
most common lag time. This most common lag time is a good initial value because, for
the most part, lag times change little throughout an experiment. The pairing result is
relatively constant for user-initialized values that vary by as much as 0.25 seconds, but
the robustness of this algorithm is also determined by the concentration of particles
that transit the cantilever system. High particle concentrations increase the number
of mispairings and can result in fewer successful pairings than an experiment with
lower concentration.
An example of two peak pairs are shown in Fig 3-9. A diagonal motion within
the scoring matrix indicates a match and a vertical or horizontal motion causes the
algorithm to discard either the current or previous pair based on closeness to the
predicted lag time. This procedure ensures that each peak is used in no more than
one pair. The predicted lag time evolves through the pairing procedure in order
to account for changes to flow rates during an experiment. One advantage to this
lag time-based approach is that peak pairs are formed without knowledge of peak
height. This is the most naı̈ve approach, and estimates of particle properties known
beforehand could be used to discard mismatches. For example, if it is known that
the particles are more dense than both fluids, then pairs with positive peaks may be
discarded. In contrast to the Needleman-Wunsch algorithm, negative scores may be
excluded and reduce the number of calculations. Negative scores mean the SMR2
peak occurs before the SMR1 peak! Of course, this is physically impossible and is a
result of the algorithm calculating lag times for all possible, even wrong, peak pairings
from which it will determine the optimal alignment to report as the final result. Also,
scores are calculated during matrix initialization without consideration of the nearest
neighbors’ values because one pair formation should not influence another. As the
datasets grow, it is helpful to illustrate this scoring algorithm geometrically (Fig 358
Figure 3-9: Two accepted peak pairs. The peak height (displayed in lower right
corner) is calculated using the baseline at the peak minimum (black point) and filtered
data (blue line, Savitzky-Golay with a 5 and 15 point window). The raw data are
shown in yellow. The lag time for each pair is indicated in the lower right corner.
59
10). These displays allow for rapid assessment of algorithm performance and aid in
experiment design.
Figure 3-10: Geometric display of dual SMR scoring matrix. (A) For larger
datasets, the scoring matrix (Fig 3-8A) may be displayed as a color map in which
the color indicates the absolute value of the lag time between two peak pairs. The
algorithm then forms peak pairs by tracing through the matrix and following a similar
color. (B) Alternatively, the axes may be plotted with respect to time. In this case,
the pairs are formed by finding the pairs that lie closest to y=x+lag time (red line),
where the lag time is the user-initialized, predicted value. Both of these displays are
generated with the same datasets and peak pairing algorithm.
3.4
Sources of measurement error
Two sources of dual SMR error inherent in cantilever geometry and the method
are: (1) position-dependent error and (2) error caused by the choice of fluid density.
Position-dependent error comes from the variable path a particle can take at the cantilever tip. It causes an uncertainty in the buoyant mass measurement, and increases
with increased buoyant mass (see §5.8 for details). Fluid density choice influences
the accuracy of the linear extrapolation (Fig 3.1) required for each single-cell density
measurment. The cell volume (slope) is known with increased certainty if the distance
between the points is large, and the cell density (x-intercept) is known with increased
certainty if the points are close to or “bracketing” the cell density (see §3.4.1 for
details).
60
3.4.1
Effect of fluid density choices on measurement error
Measurement error is minimized through careful selection of the fluid densities. For
cells, the measured fluid in the first cantilever is nearly always medium because it is
drawn directly from the sample vial. This medium sample remains unchanged until
it reaches the microchannel T-junction where a fluid of different density mixes with
the cell sample via diffusion. Cells spend ∼3-5 seconds in this fluid mixture, which
is only enough time for an osmotic shock response. Potential shock is avoided by
using biologically-compatible methods to change fluid density (see §5.7 for appropriate high-density fluids and suggested methods to determine the biological impact of
longer term exposure). Fig 3-11 illustrates how the values for fluid density affect
measurement error. In summary, as the difference between the first and second fluid
densities increases, the measurement error decreases. For the volume measurement
this improvement is independent of the absolute values of the fluid densities (evident
in Equation 3.1), but for the density measurement the improvement is dependent on
absolute fluid density. If we consider the measurement concept in geometrical form
(Fig 3-1), we are reminded that as the distance between the two data points increases,
the accuracy with which the slope of a line may be determined also increases, and the
accuracy of determining the line’s x-intercept is determined by the absolute placement of these two points. The slope of the line and x-intercept each correspond to
the particle’s volume and density, respectively. Since the fluid density in the first cantilever is usually medium, the density at the second cantilever is the only fluid that
may be altered and it is best to render the second fluid as dense as possible, therefore
creating the largest fluid density difference. The accuracy in the volume measurement
will be determined by this fluid density difference and the accuracy in the particle
density measurement can improve further if the two fluid densities “bracket” the particle density (one density is above and one below that of the particle, Fig 3-11 open
circles). A less favorable approach is to make the second fluid density close to that
of the particle, but this reduces signal amplitude.
61
Figure 3-11: The choice of fluid density affects the accuracy to which particle properties may be calculated. Calculations shown are a simulated population of particles for
which the actual mean and standard deviation of the properties are indicated by the
black lines. As the difference between the first and second fluid densities increases, the
measurement error decreases (simulated values near the black lines). This decrease is
independent of the density of the first fluid for volume measurements (data are randomly colored), but dependent for density measurements (data are in order of color).
Open circle measurements indicate instances where the two fluid densities “bracket”
the particle density (one density is above and one below that of the particle’s).
62
3.4.2
Measurement of dual SMR density resolution
In order to assess the dual SMR’s density measurement error, we measured the density
of polystyrene beads. The bead density reported by the dual SMR is 1.0495±0.0023
g/mL
(mean±SD) (Fig 3-12) and the density of polystyrene is 1.05 g/mL. Any measured
Figure 3-12: The measured distribution of density across polystyrene beads as measured by the dual SMR. Since actual variation in density for polystyrene beads is
assumed to be very small, 0.00227 g/mL is an upper estimate of instrument error.
variation in bead density is an upper estimate of the dual SMR density measurement’s
resolution because it includes both measurement error and actual density variation.
It is not known how density varies across polystyrene beads, although it is presumed
to be very small.
The small distribution of low density particles in Figure 3-12 is likely due to measurements in which a doublet (two bound beads) is measured in the first cantilever,
the doublet separates while transiting through the serpentine channel, and then each
singlet is separately measured by the second cantilever. In the peak pairing algorithm
(described in §3.3), the doublet measurement from the first cantilever is paired with
one singlet measurement in the second cantilever and the other singlet measurement
is ignored. These doublet-singlet events and associated density values may be discarded based on the large calculated volume values such erroneous pairings create
(errors as high as 100%), but are shown here as an example of a complete and unfiltered dual SMR dataset. The amount of error such events introduce into the density
63
measurement is independent of the size of the particle, but is related to the difference
between particle density and the density of the second fluid.
3.5
Cytokine-deprivation causes cell atrophy, apoptosis, and changes in density
3.5.1
Background
Multicellular organisms rely on extracellular signals, rather than nutrient availability
alone, to promote survival and coordinate cell proliferation with death. Lymphocytes,
mature white blood cells, use this control to rapidly proliferate during an immune
response and decrease in number when no longer needed, and improper regulation of
lympocyte cell number has been described in human diseases such as autoimmunity
or lymphoma [55]. Lymphocyte extracellular signals, or cytokines, can be classified
by their receptors’ chains—α-chain (IL-2, IL-4, IL-7, IL-9, and IL-15) and βc -chain
(IL-3, IL-5, and GM-CSF) [52]—and there are several reports of overlap in the pathways activated by these receptors. Activation of the IL-3 receptor (IL-3R) promotes
phosphatidylinositol-3 kinase (PI3K) activity [65], but the exact mechanism of IL-3R
activation of PI3K is not yet clear [52]. PI3K activates its downstream protein kinase
Akt, which contributes to glucose metabolism as a mediator between extracellular
signals and Glut1 levels and localization [65]. Glut1 is a transmembrane protein that
transports glucose into the cell via facilitated diffusion, and its membrane concentration is regulated through a balance between endocytosis and trafficking back to
the membrane [65]. Thus, IL-3, through IL-3R activation, promotes glucose uptake
through localization of Glut1 to the membrane. A relationship between extracellular
signal and glucose uptake has also been reported for other cytokines, in particular,
IL-7.
Upon extracellular signal depletion, glucose intake decreases, cells undergo atrophy and if the cells are not re-stimulated, they commit to death. During the early
stages of cytokine deprivation, decreased glucose levels cause decreased cell size and
64
protein content [56]. Later, the mitochondria break down and release cytochrome c
and other pro-apoptotic proteins from the inner mitochondrial space that, combined
with nonfunctioning mitochondria, cause cell death [55]. The connection between
decreased nutrient uptake and mitochondria function has been observed in multiple
cell lines, including IL-4 and IL-7 dependent primary lymphocytes [54] and murine
FL5.12 pro-B cells [56].
Apoptosis is a form of cell death required for healthy development and maintainence of multicellular organisms, including normal immune response. Although
there are both extracellular and intracellular apoptotic triggers and different apoptotic pathways, some of which require synthesis and others that do not (caspasedependent), there are certain morphological changes that universally occur. One
early event of apoptosis is cell shrinkage, or apoptotic volume decrease (AVD), which
is the result of intracellular ion and water loss [12]. The significance of AVD in apoptosis is still unclear, with reports by some that it is both necessary and sufficient[22, 43]
and reports by others that ion fluxes alone are adequate [12]. Chromatin condensation and permeabilization of the nuclear envelope follow AVD, and in the final stages
of apoptosis, the cell membrane breaks down to package cellular contents into small
vesicles. The vesicles, or apoptotic bodies, are phagocytosed by surrounding cells
with minimal immune response.
3.5.2
Cell density as a function of starvation
We measured single cell density with the dual SMR to characterize how cell density changes upon cytokine deprivation. IL-3 was removed from the medium of a
murine, IL-3 dependent, pro-B cell line (FL5.12), and density was monitored at fixed
timepoints over 48h. Volume was measured with the Coulter counter. We observed
volume to decrease, as expected during atrophy, but density increased during the first
24h of IL-3 deprivation. Rathmell, et al [56] state that “cell size can be an indicator
of net cellular metabolism,” and we believe that volume combined with density may
be a powerful two-parameter index that more accurately describes the state of the
cell.
65
Figure 3-13: FL5.12 cell density and volume upon cytokine-deprivation (A)
Following cytokine deprivation, FL5.12 cells increase in density for the first ∼24
hours, followed by a rapid decrease in density. The single-cell density measurements
are shown as single points and the data are summarized in a box-and-whiskers format, where the center line, box edges, and whiskers are the median, quartiles, and
one standard deviation, respectively. The change in density median is significant
(p0.001) as supported by the Mann-Whitney rank sum test, a non-parametric form
of the t-test. (B) Cell volume continuously decreases following cytokine deprivation.
66
It is important to understand that size adaptation to poor environment occurs
on two different timescales, only one in which changes to cells’ physical properties
have significance in cell survival. Size adaptation can occur by either (1) A gradual
process over several cell generations to ultimately promote cell survival through poor
conditions (the example shown in this section), and (2) A rapid size change for which
nearly all cells die in response to an osmotic shock or a decrease in the cell’s ability to
regulate its membrane potential (a likely example of this is provided in §4.2.3). In this
second circumstance, the size change is a passive response to the environment and
often occurs in seconds, there is no physiological advantage, and the cell is destined to
die. In the first example, however, there are several advantages for a cell population
to gradually decrease its total volume and increase density when challenged by the
environment. These physiological changes effectively increase the concentration of
cellular components and increase reaction rates, particularly ATP synthesis, but it
is not clear if this increased concentration is localized, or how proximity limits ATP
synthesis. Another advantage to decreased volume is the resulting decreased surface
area. One of the most energetically intensive cellular processes is maintainence of
polarization across the cell membrane and reduced membrane area will have a lower
energy requirement. Finally, decreased surface area may make membrane lipids available for energy and lipids are a high-energy source of nutrients. Interestingly, the G0
cell state is nearly always smaller than a cell normally progressing through the cell
cycle and may further support the idea that smaller size enables higher survival rates.
Additional studies to further investigate the idea that small cells better survive poor
conditions would include detailed analysis of cell membrane uptake and trafficking
during size adaptation as well as how the adaptation depends on cell cycle position.
Future directions for the dual SMR include improved mixing and higher throughput, but we also envision an integrated cell sorting mechanism or ordered trap for cell
tracking and downstream analysis.
67
68
Chapter 4
Single cell density identifies cell
state
We have implemented Archimedes’ method in a microfluidic system to measure the
density of individual cells with a precision of 0.001 g/mL at a rate of ∼500 cells per hour.
We find that the intrinsic cell-to-cell density variation is nearly 100-fold smaller than
the mass or volume variation, and by simultaneously measuring density and mass, we
identify distinct subpopulations of diseased and healthy cells that are indistinguishable by mass and volume alone.
4.1
Introduction
Evidence suggests that cells adjust their mass to volume ratio during important processes such as cell cycle progression [67], apoptosis [45, 68], differentiation [37, 44],
disease state [64], and malignant transformation [13, 58]. While important insights
have come from tracking single cell volume during such processes, and methods for
monitoring cell mass are emerging, there currently does not exist a means for measuring the density of individual cells with meaningful precision.
Existing density measurements generally rely on buoyant force to transport cells
to a location where the surrounding fluid density most closely equals the cell’s density.
Even when sped up by centrifugation, lengthy exposure to concentrated solutions of
69
the substance used to construct the density gradient may inadvertently affect the
density and viability of the cells. Density gradients also have a fundamental tradeoff between dynamic range and resolution, and construction of a high-resolution but
narrow-range density gradient requires that the cell density be known a priori. Combined with the difficulty of tracking single cells in centrifuge tubes, these limitations
have precluded the use of density gradient centrifugation for quantifying the density
of individual cells.
The ideal method for measuring a single cell’s density would not rely on buoyant
force to slowly push the cell to a position with matched density, but would measure
the buoyant force on a cell directly, in any desired fluid, and then use this to calculate
not only the density but also the mass and volume of the cell. Remarkably, such a
method was used around 250 BC by Archimedes of Syracuse, who was asked by the
king to determine whether the royal crown was made of pure gold. One version of
this story suggests that Archimedes measured the density of the crown by hanging it
in a fluid and using a balance to measure the submerged crown’s buoyant mass:
density of f luid
buoyant mass of crown = absolute mass of crown 1 −
(4.1)
density of crown
By measuring the buoyant mass of the crown in two fluids of different known densities
(for example, water and air), Archimedes could then calculate the density of the crown
and compare it to the known density of pure gold.
In this work we use Archimedes’ original method in a microfluidic system to measure the density of single cells. This approach requires both a system to weigh single
cells with femtogram precision and a method to rapidly exchange the fluid surrounding a single cell during laminar flow. By weighing each cell in two different fluid
densities and applying Archimedes’ method, we obtain not only single-cell density
but also single-cell volume and absolute mass. By measuring many cells in this manner, we obtain the distributions of densities, volumes, and masses in a population.
Finally, by measuring cells over time, we can also obtain information about how cell
density, volume, mass, and their distributions change as the cell grows or responds
70
to stimuli. All together, this provides what is arguably the most complete metric of
cell size currently available.
4.1.1
A microfluidic implementation of Archimedes’ method
The “balance” we use to weigh cells in two different fluids is the Suspended Microchannel Resonator (SMR), a microfabricated microfluidic mass sensor [16]. As
shown in Figure 4-1C and 4-2, the SMR consists of a silicon cantilever containing an
embedded microfluidic channel.
The cantilever oscillates at a frequency that is proportional to its mass, and a
cell passing through the embedded channel changes the resonance frequency of the
cantilever by an amount proportional to the buoyant mass of the cell. Previous
work with the SMR showed that the average density of a population of cells can be
calculated from buoyant mass measurements [27, 14] and that yeast exhibit cell cycledependent variations in average cell density, [14] but these methods cannot measure
the density of single cells or derive statistics about the density distribution.
4.2
4.2.1
Results and Discussion
Single particle mass, density, and volume
To measure single-cell density with the SMR, the device is first loaded with two
different fluids: one containing the cells of interest in any buffer or medium, and
another with the same tonicity as the first solution but greater density. A cell’s
buoyant mass in the first fluid is recorded as a peak in the resonance frequency of the
SMR while the cell passes through the resonating microchannel. The cell then enters
the second fluid, where the faster flow rate quickly dilutes the first fluid surrounding
the cell. Diluting the fluid around the cell takes only ∼1 s, a remarkably fast exchange
for a free-flowing cell in laminar flow conditions. The direction of flow is then reversed,
and the cell passes through the cantilever a second time to measure its buoyant mass
in the second fluid. The cell spends very little time (as little as 3 s) in contact with the
71
Single cell buoyant mass
A
Buffer 1
Absolute mass
Density
Fluid density (g/mL)
Cell’s buoyant mass
in less-dense fluid
Volume
Cell’s buoyant mass
in more-dense fluid
D
Buoyant mass in buffer 1
Buoyant mass in buffer 2
1
Bu
ffe
r
2
r
ffe
Bu
E
Buffer 2
Figure 4-1: (A) Applying Archimedes’ method to measure single cell mass, volume,
and density. By weighing a cell in two fluids of different density and plotting the linear
relationship between buoyant mass and fluid density, the absolute mass, volume, and
density of the cell can be determined from the Y-intercept, slope, and X-intercept,
respectively. (B) One minute of the raw resonance frequency of the Suspended Microchannel Resonator (SMR) for 12 cell density measurements. On this scale, only
the fluctuations caused by the switching between two different buffer densities are
visible. (C) Close-up of the measurement of a single erythrocyte, showing (D) a ∼30
Hz downward peak in the SMR resonance frequency as the cell surrounded by Buffer
1 is measured, then a large ∼5000 Hz decrease as more-dense Buffer 2 passes through
the cantilever, and finally (E) a ∼10 Hz upward peak as the cell surrounded by Buffer
2 is measured.
72
Figure 4-2: Step-by-step illustration of single cell mass, density, and volume measurement using a single SMR.
73
final.jpg
Figure 4-3: Close-up of the measurement for a single L1210 cell in a 15x20µm SMR.
The two insets show the buoyant mass measurement of the same cell in two different
fluid densities. Since the cantilever microchannel:bypass crosssection ratio is 1:47 for
the 8x8µm devices and 1:7 for the 15x20µm devices, the time required for fluid mixing
is increased in this measurement and instability due to incomplete mixing is observed.
74
high-density fluid before its buoyant mass is measured. From these two measurements
of buoyant mass, the absolute mass, volume, and density of the cell can be calculated
(Figure 4-4A). This process takes ∼5 s per cell, and the system can measure ∼500
cells/h.
To validate our method, we measured beads with known density and size. Figure
4-4A shows the bead volume, mass, and density distributions for a sample of 5 µm
diameter polystyrene beads. The coefficient of variation (CV) of bead density is
Figure 4-4: (A) Bead mass, volume, and density distributions for a population of 5.0
µm diameter polystyrene beads (n = 1,069, Duke Scientific), and (B) a scatter plot
of bead mass vs. density. Error bars are ± two standard deviations of the mean
(95% confidence interval). (C) Erythrocyte mass vs. density for 690 cells from a
healthy culture (left) and an equal number of cells from a culture containing ∼12% P.
falciparum-infected erythrocytes (less-dense infected cells lie to the left of the ellipse).
Error bars show the 95% confidence interval for each point. (D) Single erythrocyte
mass vs. density for an individual with suspected thalassemia who also received a
transfusion of normal (non-thalassemic) blood five days prior to analysis (red; n =
502 cells), and a random non-thalassemic, non-transfused individual (black; n = 502
cells). The patient’s own erythrocytes (red) are offset from a normal patient’s erythrocytes (black), except for a small number of normal erythrocytes the thalassemic
patient received during the transfusion (red points clustered on black points). (E)
Erythrocytes from an individual with sickle-cell anemia and a recent blood transfusion (red; n = 502 cells) to the same non-transfused individual as before (black; n
= 502 cells). The widening of the distribution of erythrocyte densities in sickle cell
anemia is consistent with other studies14 and may reflect variation in the extent to
which each cell is sickled.
75
almost thirty times smaller than the CV of bead volume or mass. The error bars
on the plot of bead mass vs. density (Figure 4-4B) provide an upper estimate of
the resolution of our method: 3 pg absolute mass, 3 fL volume, and 0.001 g/mL
density (± two standard deviations). To validate our method using a cell sample, we
measured Plasmodium falciparum malaria-infected erythrocytes (Figure 4-4C) and
observed the expected fraction of low-density infected erythrocytes.
4.2.2
Erythrocyte density is determined by more than environmental conditions
In a small-scale blood study, we measured single-cell volume, mass, and density for
∼500 human erythrocytes from each of 16 patients. Hemoglobin concentration and
erythrocyte volume are well known to be altered in various diseases. Since hemoglobin
comprises about one-third of the mass of an erythrocyte, we hypothesized that erythrocyte density may also correlate with disease states. In addition, nine of these
individuals received recent blood transfusions prior to analysis. By analyzing blood
from transfusion recipients, we explored whether the combination of single-cell volume, mass, and density could be used to distinguish host and donor erythrocytes.
This ability could then be used to assess the survival of transfused cells or possibly identify athletes who have received performance-enhancing transfusions (blood
doping) [26].
Figures 4-4D and E show plots of erythrocyte mass vs. density for two transfusion
recipients. The sample in Figure 4-4D (red points) is from an individual suspected to
have a thalassemia trait, a genetic condition that causes smaller erythrocyte volumes.
Our measurements confirm this and also show smaller erythrocyte masses and densities compared to a random non-thalassemic, non-transfused patient (black points).
In addition, a small fraction of normal-mass, normal-density erythrocytes in the thalassemic individual’s blood is evident and corresponds to the healthy cells the patient
received via transfusion 5 days prior to analysis. This diagonally offset subpopulation
could only be detected in a multi-parameter measurement as demonstrated, and not
76
by mass, volume, or density alone. The sample in Figure 4-4E (red points) is from
a patient with sickle cell anemia who received a transfusion of normal blood 39 days
before analysis. The widened erythrocyte density distribution is in agreement with
earlier studies [57] and may reflect variation in the extent to which each cell is sickled.
To assess how an individual’s single-cell density changes with time, we obtained two
additional samples of blood drawn from the thalassemic patient 1 and 4 days later
than the sample analyzed in Figure 4-4D. The patient’s erythrocyte mass, volume,
and density distributions remained essentially unchanged over 4 days (Supplementary
Figure A-11). These measurements show that cell density is by far the most tightly
regulated aspect of cell size, but meaningful cell-to-cell variation in density exists and
our method can discriminate the small fraction of transfused blood cells that are only
∼1% more dense than an individual’s own blood cells.
Figure 4-5 presents a comparison of erythrocyte density distribution measurements
p = 0.001
14
12
10
Normal
(n = 7)
Transfused
(n = 7)
16
p = 0.001
14
12
10
Normal
(n = 7)
Transfused
(n = 7)
CV of erythrocyte density (%)
16
CV of erythrocyte mass (%)
CV of erythrocyte volume (%)
between seven transfused and seven non-transfused individuals. To focus only on the
0.8
p = 0.008
0.6
0.4
Normal
(n = 7)
Transfused
(n = 7)
Figure 4-5: Distribution widths of single-cell erythrocyte volumes, masses, and densities for seven individuals who received blood transfusions up to 8 days before analysis
(“Transfused”), and seven individuals who did not receive transfusions (“Normal”).
As expected from earlier studies [9], transfusion increases the coefficient of variation
(CV) of an individual’s erythrocyte volumes; we also find that transfusion increases
the CV of an individual’s erythrocyte masses and densities as well. P values are obtained from the Mann-Whitney U test, and box center, edges, and whiskers represent
median, interquartile range, and total range, respectively.
effect of transfusion on the erythrocyte distributions, individuals with pre-existing
conditions that had dramatic effects on the distributions (such as the thalassemic and
sickle cell patients in Figures 4-4D and E) were not included in this comparison. We
77
found that receiving a blood transfusion significantly increases the erythrocyte volume
distribution (p < 0.01; Mann-Whitney U test), which is consistent with previous
studies [9]. We also measured a similar increase in the erythrocyte mass distribution
(p < 0.01) and a smaller but still significant increase in the erythrocyte density
distribution (p < 0.01), all of which are evident regardless of the statistical metric of
distribution width used (Supplementary Figure A-7). These measurements suggest
that the mass, volume, and density of erythrocytes remain largely unchanged even
after the cells have spent days in another individual. In addition, these 14 individuals’
mean erythrocyte densities do not obviously correlate with the mean cell volume,
mean cell hemoglobin content, or hematocrit, as measured by a clinical instrument
(Supplementary Figure A-8). The erythrocyte density distribution width correlates
only weakly with the cell volume and mass distribution widths (Supplementary Figure
A-10). These observations suggest that cell density is not merely a function of cellular
environment or the concentration of certain cellular components, and that cell density
distribution width may be an independent and useful diagnostic.
4.2.3
Density identifies early stages of apoptosis
Our method can also monitor the physical properties of cells over time, as the cells
proceed through their cell cycles or respond to changes in the environment. Using a
related device geometry, we measured the properties of single cells from a synchronized
culture of mouse lymphocytic leukemia cells (L1210) before and after treatment with
staurosporine (STS). STS is a general kinase inhibitor that is commonly used as an
inducer of the intrinsic apoptosis pathway, a form of programmed cell death initiated
by internal injury to the cell [22]. One early event of apoptosis is cell shrinkage,
or apoptotic volume decrease (AVD), which was previously discussed in §3.5.1. We
observed a ∼25% decrease in mean cell mass and volume and a corresponding ∼1%
increase in density after just 20 minutes of STS treatment (Figure 4-6). Although
the percent change in cell mass and volume is larger than the change in density,
the large cell-to-cell variability in mass and volume masks this change. In contrast,
the small increase in density accompanying STS treatment remains obvious against
78
Lymphocyte volume (fL)
A
1500
B
Staurosporine
in DMSO added
DMSO added
1000
500
Lymphocyte mass (pg)
0
1500
1000
500
Lymphocyte density (g/mL)
0
1.100
1.080
1.060
0
40
80 120
Time (min)
160 0
40
80 120
Time (min)
160
Figure 4-6: Time-course data of single-cell masses, volumes, and densities of L1210
mouse lymphocytic leukemia cells before (black) and after (red) the addition of either
staurosporine (STS) in DMSO (A) or a DMSO-only control (B). Shaded areas show
the mean ± two standard deviations for the pre-treatment data. As expected from
earlier studies, the average lymphocyte volume decreases shortly after STS treatment.
We also observe a corresponding post-treatment decrease in lymphocyte mass, and a
much more statistically-significant increase in lymphocyte density. In contrast, cells
in the DMSO-only control remain unchanged post treatment (B).
79
the background of small cell-to-cell variability in density. The rapid and widespread
increase in cell density suggests that the cells initially decrease in water content rather
than increase in biomass, because biomass synthesis requires hours and a volume
increase. Cells treated with an equal volume of DMSO did not exhibit a change
in density and the 2 µM concentration of STS does not contribute significantly to
the solution osmolarity (> 300 mOsm). These early cell density changes may be
indicative of constant cell biomass during AVD, which has not yet been described, or
apoptosis-unrelated effects of staurosporine. Nevertheless, the measurement further
demonstrates density as an important parameter in distinguishing cell state and our
method’s ability to measure the properties of large cells (> 200 fL) with high precision
at the single-cell level.
We have combined a tool for weighing single cells with microscale fluid manipulation to develop a rapid and simultaneous measurement of the density, mass, and
volume of large numbers of single cells. Our method can discriminate the small fraction of transfused blood cells that are only ∼1% more dense than an individual’s own
blood cells. Our technique can also detect a change in cell density that is statistically
more significant than the well-known change in cell volume accompanying apoptosis. Methods for measuring fundamental biomechanical and biophysical attributes
of single cells have consistently provided valuable insights into cell biology, and we
anticipate that density, a fundamental property of all cells, will similarly prove to be
useful for identifying, distinguishing, and studying single cells.
4.3
Materials and Methods
Instrument set-up and fluid manipulation A schematic of the experimental
system is shown in Supplementary Figure A-6. The system contains two parallel
paths for fluids (the red and blue paths in Supplementary Figure A-6). These two
fluid paths are connected through the mass-sensitive resonating microchannel in the
SMR. By applying a pressure differential across the resonating microchannel, the
contents of either fluid path can be sent through the resonating cantilever and into
80
the other fluid path. Downstream of the SMR, a regulated pneumatic vacuum and
two computer-controlled solenoid valves direct the flow of fluid through the system.
During a typical experiment, cells are prepared in any buffer or mediim at a
concentration of 1 × 106 to 1 × 108 cells/mL and connected to the red path via
capillary tubing inserted into the flask (Supplementary Figure A-6). The blue path
is connected to a flask containing ∼1 mL of an otherwise-identical buffer with a
different density. To avoid inducing osmotic changes in the cells, the osmolality of
the two fluids should be as similar as possible. Solutions of colloidal silica particles
coated with polyvinylpyrrolidone (“Percoll,” Sigma-Aldrich) have high density (1.130
g/mL) and low osmolality (< 25 mOs/kg H2O); substituting these solutions for water
in a buffer or medium recipe increases the fluid’s density without significantly altering
its osmolality.
To load the cells and fluids into the system, the solenoid valves are switched on to
apply high (∼20 inHg) vacuum to both downstream waste vials. Within one minute
the red path fills with cells in medium and the blue path fills with alternate-density
medium.
To measure cells, the magnitude of the downstream vacuum is first decreased to
∼5 mmHg and the solenoid valve connected to the red path is then switched off; this
slows the flow of cells in the red path, but the flow of alternate-density medium in
the blue path continues (Supplementary Figure A-6A). The difference in pressures
between the two fluid paths causes a cell to flow from the red path through the
resonating microchannel and into the blue path. The buoyant mass of the cell in
medium is recorded as a peak in the resonance frequency of the SMR, and the cell
enters the alternate-density fluid in the high-flow blue path (Figure A-6B). The states
of both solenoid valves are then reversed, so that applied vacuum drives high flow in
the red path but flow slows in the blue path. This drives the cell, now surrounded by
alternate-density fluid from the blue path, back through the resonating microchannel
and into the red path (Figure A-6C). The buoyant mass of the cell in the alternatedensity medium is recorded from the peak in the SMR resonance frequency, and the
cell reenters its original medium in the high-flow red path. At this point the computer
81
program controlling the system waits for 1 s to ensure that the cell has been flushed
down the red path (Figure A-6D), then reverses the states of the solenoid valves again
in preparation for measuring the next cell (Figure A-6A again). This process takes
∼5 s per cell. Every 10 minutes the regulated vacuum magnitude is increased to ∼25
mmHg for one minute to load fresh cells from the flask into the SMR. The throughput
of the system is ∼500 cells per hour.
Data processing. The resulting SMR resonance frequency data contain one pair
of peaks for each cell measured. The larger 15 µm by 20 µm resonating microchannels
used to measure the L1210 mammalian lymphocytes (Figure 4-6) yield peaks ∼100 ms
wide; these peaks are well resolved and can be analyzed by smoothing the frequency
data with a Savitzky-Golay filter and fitting a second order polynomial to the peak
tip and a line to the baseline. The resulting peak height is proportional to the
buoyant mass of the cell in the particular medium, and the baseline frequency is
proportional to the solution density (calibration details below). The smaller 8 µm by 8
µm resonating microchannels used to measure the polystyrene beads (Figures 4-4AB),
malaria-infected erythrocytes (Fig. 4-4C), and transfusion recipient erythrocytes (Fig
4-4DE and 4-5) yield peaks only ∼10 ms wide; the tips of these peaks are not resolved
well enough to be analyzed in the same way. Instead, each peak is fit to a calculated
peak shape based on the work of Dohn et al.18 The calculated peak shape is a function
of the cell’s buoyant mass, the solution density, and other terms describing the peak
and baseline. By using the Nelder-Mead method to minimize the sum of squared
differences between the experimental and calculated peaks, the cell’s buoyant mass
and the solution density can be determined.
System calibration. Two calibrations are necessary before measuring cell density with the SMR. The first calibration measures the response of the SMR to a known
buoyant mass. Beads with a known volume and density are suspended in a fluid of
known density and passed through the resonating microchannel. The resulting peaks
are analyzed as described above to determine the mass calibration constant. In practice, this constant remains relatively unchanged throughout the life of a SMR device,
so it typically is determined only once. The second calibration measures the response
82
of the SMR to fluid with a known density. Two or more solutions with precisely
known densities (for example, sodium chloride solutions prepared gravimetrically)
are loaded into the resonating microchannel. Fitting the resulting plot of solution
density vs. baseline resonance frequency to a polynomial provides a function for converting SMR resonance frequency to solution density. In practice, the lowest-order
term of the polynomial (the Y-intercept) can change significantly over time due to e.g.
accretion of mass on the inside walls of the resonating microchannel. The resulting
error directly affects the measured cell density (for example, a Y-intercept term that
is 1% too high will result in a measured cell density that is 1% too high). For this
reason, we regularly perform a quick and simple single-solution density calibration
(to determine the Y-intercept).
Polystyrene bead measurements. For the bead measurements (Figures 44AB), 5.0 µm diameter polystyrene beads (Duke Scientific) were diluted to a concentration of X beads per mL in 1x phosphate buffered saline (PBS) containing 0.1%
polysorbate 20 (“Tween-20,” Sigma-Aldrich).
Malaria culture measurements. For the malaria culture measurements (Figure 2C), Plasmodium falciparum 3D7A parasites (Malaria Research and Reference
Reagent Resource Center, American Type Culture Collection, Manassas, VA) were
cultured in human erythrocytes (Research Blood Components, Brighton, MA) in
RPMI-1640 complete medium as described elsewhere. ∼1 mL of each culture (latestage infected and healthy) was diluted into 10 mL of a simplified RPMI-1640 medium
(prepared by dissolving 10.44 g RPMI-1640, 5.44 g HEPES, and 2.00 g NaHCO3 in
water for a final volume of 1.0 L). A small volume of the same medium was prepared substituting Percoll for water; this was used as the more-dense medium in the
SMR. The diluted cultures were maintained at 37◦ C and stirred gently during ∼2 h
of analysis.
Erythrocyte measurements. For the transfusion recipient erythrocyte measurements (Figures 4-4DE and 4-5), fresh whole blood was obtained from seven patients who had received recent transfusions and from seven patients who had not. For
each sample, 5 µL of blood was diluted into 10 mL of 1x PBS. To make the more-dense
83
buffer, 100 µL of 10X PBS was combined with 900 µL of concentrated Percoll1 . The
diluted blood samples were maintained at 25◦ C during ∼2 h of analysis. A second
capillary tube inserted into the diluted blood sample bubbled a gentle stream of air
into the vial and kept the cells in suspension during analysis.
Mouse lymphoblast culture measurements. For the L1210 measurements
(Figure 4-6), cells were grown at 37◦ C in L-15 medium (Gibco) supplemented with
0.4% (w/v) glucose, 10% (v/v) fetal bovine serum (Sigma-Aldrich), 100 I.U. penicillin,
and 100 µg/mL streptomycin. Cells were passaged every 2-3 days to maintain a cell
concentration of ∼50,000 mL−1 . For the SMR measurements, cells from culture were
spun down, resuspended in fresh pre-warmed medium at a concentration of ∼100,000
mL−1 , and delivered to the SMR. The more-dense buffer consisted of 45% liquid food
coloring, 45% 2x L-15 Percoll medium (pH 7.2), and 10% L-15 medium. L-15 Percoll
medium is identical to the cell culture medium with the exception of 50% Percoll (v/v)
and the use of powdered (13.8 g/L, Sigma-Aldrich) rather than liquid L-15 medium.
After 1 hour of measurement, cells were treated with 2 µM staurosporine or an equal
volume of DMSO (mock-treated control) and measured for an additional hour. The
SMR and sample were maintained at 37◦ C. The cell sample (described below) was
added to a glass sample vial such that the fluid level did not exceed 0.5 cm, which
minimizes the disturbance to cell metabolism. A centrifuge tube containing ∼1 mL
of replacement fluid was placed inside of the glass sample vial to deliver these two
fluids at equal pressure.
The larger 15 µm by 20 µm resonating microchannel used to measure the L1210
cells was interfaced to cells and medium as shown in Supplementary Figure A-6, but
using upstream pressure instead of downstream vacuum to drive fluid flow through
the system. Three of the four SMR device ports were maintained with a single
pressure regulator. Fine corrections to the pressure at the start of each experiment
were individually made to these ports by changing the fluid vial height. The fourth
1
Concentrated Percoll was prepared by filling 5 mL syringes with Percoll, capping the syringes,
and placing the syringes oriented plunger-up at -20◦ C for at least 16 hours. The syringes were then
transferred to a freezer and allowed to thaw at 4◦ C over at least 16 hours. A freeze-thaw cycle causes
a density gradient to form within a tube of Percoll. The bottom ∼1 mL (the densest fraction) was
then dispensed from the syringes and used in the above protocol.
84
port alternates between a low and high pressure source via a solenoid valve (SMC
USA) that responds to the SMR resonant frequency. Actuation of this valve controls
fluid flow direction through the SMR. Following each flow reversal, a 400ms ∼10%
increase in sample pressure was applied to flush away partially mixed fluid and bring
in new cells. Every 4.25 minutes the tubing was flushed with a high-pressure (∼70
kPa) rinse for 45 seconds and the sample vial was gently shaken to mix the cells. No
measured cell spent more than 4.25 minutes in the microfluidic system.
85
86
Chapter 5
SMR system development and
analysis details
5.1
Peak height determination for buoyant mass
measurement: fitting and filtering
The accuracy of the SMR’s buoyant mass measurement is a direct result of how the
peak height is determined from the recorded frequency. One approach to peak height
determination is to find each peak and fit the raw data to the analytical function for
a cantilever loaded with a point mass. This function is adapted from [19]:
s
ω∆m =
ω2
−1
U (z∆m )2
1 + ∆m ·
,
m0
(5.1)
where ω∆m and ω are the resonance frequencies of the loaded and unloaded cantilever,
respectively, ∆m is the buoyant mass of the particle, m0 is the mass of the unloaded
cantilever, U is the beam displacement given in Eqn 5.6, and z∆m is the path of
the particle along the cantilever length (example given in Fig 5-1A). For simplification, the particle trajectory (z∆m ) does not consider the additional distance caused
by the cantilever microchannel’s corners, which is small compared to the cantilever
length. One advantage to using the analytical function is that it considers the entire
87
Figure 5-1: Analytical function and Savitzky-Golay filtering of peaks. (A)
Particle trajectory along the length of the cantilever used in solving the analytical
function. Cantilever length = 321 µm. Dashed lines in parts ABC indicate where
the particle entered and exited the cantilever. (B) Analytical prediction for a particle
passing through the cantilever (black line) with added white noise for simulated data
(yellow line). (C) Savitzky-Golay filtering (window width = [15 : 45]) of simulated
data. The peak tip (inset) decreases with increased filter window width, even when
the filter window width is <10% of the peak width! Distortions at the peak edges
(indicated by arrows) occur with larger filter windows and when peak height errors
are 40% and more. (D) As the Savitzky-Golay filter window width increases, the
error in peak height also increases. This error is peak width- and height-dependent
because as the sharpness of the peak increases, the filter has a more pronounced
smoothing effect. Thus, filter settings should be optimized for the largest and fastest
peaks within an experiment. These simulations vary with each iteration, but the
general trends are consistent.
88
peak dataset, rather than only the baseline and peak tip. This makes the analytical
function ideal for very fast or very large peaks, which are subject to distortion when
smoothed. One major drawback to the analytical function is that it cannot account
for peak asymmetries that occur with particle sticking or momentary changes to flow
rate. In this case, data smoothing can outperform the computationally expensive
peak fitting approach.
A Savitzky-Golay smoothing filter [61] performs polynomial fits to a moving window and better preserves sharp changes in data (e.g., peaks) as compared to a moving
average. However, marginally incorrect Savitzky-Golay filter settings can rapidly degrade peak height (Fig 5-1C) and with little warning. Degradation rates depend on
peak height and width (Fig 5-1D), and filter settings should be optimized for the
largest and fastests peaks within an experiment. For cells, there can easily be a
greater than two-fold buoyant mass change across the population and peak widths
may change as much as five-fold during an experiment. A direct comparison between raw and filtered data for every peak measurement is critical in the accurate
determination of particle buoyant mass.
5.2
Fluid density calibration and density measurement of an arbitrary fluid
In order to use buoyant mass to calculate single-particle density or the average density
of particle populations, the density of the fluid in which the particles are suspended
must be precisely known (Equations 1.1, 2.1, and 3.1). The SMR is capable of fluid
density measurements with 10−4 g/mL accuracy. To achieve this, two measurements
are made: (1) Every new device is calibrated with several solutions of known density, and (2) Before every experiment a single density standard (typically water) is
measured as the resonance frequency offset. The first measurment, the calibration
for each new device, is accomplished by gravimetrically preparing several glycerol
or sodium chloride solutions of varying concentrations and measuring the resonance
89
frequency of the SMR when filled with each of these solutions. The density of the
prepared solutions may be determined by interpolation of data provided in the CRC
Handbook of Chemistry and Physics, which reports with 10−4 g/mL precision the density of a variety of aqueous solutions. Since fluid density and cantilever properties are
a function of temperature, the calibration must be performed at the same temperature as the experiments (i.e. 37◦ C for live mammalian cell culture). Fluid density
values at temperatures not reported by the handbook may be calculated by the linear interpolation of proximal values. Careful measurement and calculation yield fluid
density standards with greater precision than commercially available salt solutions,
which are typically reported to just 0.1M precision. Once used, density standards
should be discarded because they alter with age, likely due to evaporation. Once a
baseline resonance frequency is recorded for each prepared solution, the correlation
between resonance frequency and solution density may be determined by linear regression (such as in Figure 5-2). Any error in the preparation of the density standards
is minimized by this linear regression and performing the calibration with three or
more points.
The result of the fluid density calibration is unique to the device and a specific
operating temperature, but is otherwise robust and need not be repeated. This calibration (the slope of the linear regression) is constant, but the absolute resonance
frequency measurement for a given fluid is not. In other words, it is best that the
conversions between resonance frequency baseline and fluid density are not done by
the absolute resonance frequency, but rather the resonance frequency difference between the fluid and a known standard (typically water, as shown in Figure 5-2).
Changes to the recorded resonance frequency of a fluid with constant density over
long timescales, or changes to the offset, occur as a result of the slight fluctuation
in the amount of surface-bound material. Particle “sticking” events are relatively
rare for a well passivated and smooth silicon channel (<0.1% of cell measurements)
and changes to the offset are more likely a result of non-specific binding of medium
proteins and cell debris. Although a particle sticking to the cantilever surface during
an experiment affects this offset, it is usually momentary and the addition of a single
90
particle is small when compared to the mass of fluid filling the cantilever—a 10µm
cell introduces <0.05% error to the fluid density measured by a 15x20µm SMR. A
single density standard (typically water) can be measured at the beginning of every
experiment in order to account for these fluctuations and is necessary to achieve high
precision density measurements.
Once the initial calibration and a water baseline measurement is complete, the user
can measure the density of an arbitrary fluid by calculating the difference in resonance
frequency between water and the arbitrary fluid and then use the slope of the linear
regression calculated during calibration to correlate the resonance frequency change
to a fluid density. Fluid density measurements can be calculated for every particle
that passes through the SMR system simply by following this procedure and recorded
the resonance frequency baseline for each peak height (buoyant mass) measurement.
5.3
Correction of buoyant mass to a fluid density
standard using average cell volume
In order to compare buoyant mass measurements with small variations in fluid density,
the buoyant mass dependency on fluid density requires that fluid density be either
constant, corrected for, or, at the very least, reported. One method to correct for
differences in fluid density across measurements is to use cell volume as a second
known variable and adjust all buoyant mass measurements to a single fluid density.
For comparisons between samples in §2.1, the cell buoyant mass was corrected to the
fluid density of water at 20◦ C (0.9982 g/mL) by:
mB,corrected = mB,measured + Vcell · (ρf,measured − ρwater,20◦ C ),
(5.2)
This correction is limited by how volume is measured. If volume is known on a single
cell basis, then the buoyant mass may be corrected for each cell, otherwise the same
volume must be assumed for all particles and the SMR’s buoyant mass measurement
accuracy is reduced. Although limiting, this approach is preferable to experimentally
91
maintaining fluid density across sample preparations, which is in practice difficult
to acheive with 10−4 g/mL accuracy. Differences in fluid density due to changes in
medium type, sample preparation, or system conditions all contribute to buoyant
mass variation, especially for large cells and when measurements occur months apart.
Although this correction does not significantly affect measured growth rates, it will
shift cells’ initial buoyant mass.
5.4
Density variation estimate from mean buoyant
mass and volume by the Geary-Hinkley Transformation
This section describes how a population’s buoyant mass and volume distributions may
be used to calculate the standard deviation in density. If cell volume (Vcell , referred
to as V in this section) and buoyant mass (mB ) are normally distributed random
2
) and Eqn 2.1 is simply the ratio
variables, then V∼N(µV , σV2 ) and mB ∼N(µmB , σm
B
of two normally distributed variables with the addition of a constant. Let Wparticle
represent this ratio, mB /V. Wparticle (and, it follows, particle density) may be assumed
normally distributed for any correlation of mB and V, if the coefficient of variation
(CV) in volume is <0.39 and in buoyant mass is >0.005 [32], which often holds for
cell populations. If this condition is met, the expected mean and standard deviation
of Wparticle may be calculated by a variation on the the Geary-Hinkley transformation
[34, 25] published by [32]:
2
2
Wparticle
(µ2V − z 2 σV2 ) + Wparticle (2z 2 ρσV σmB − 2µV µmB ) + (µ2mB − z 2 σm
) = 0, (5.3)
B
where ρ is the correlation coefficient between mB and V and z is the desired zscore (1.96 for 95% confidence interval). For cells, the term with the correlation
coefficient is usually insignificant compared to the term that follows and knowledge
of the correlation coefficient is not necessary. The solution to Eqn 5.3 yields the
92
probability interval for Wparticle from which the expectation (mean) and standard
deviation of Wparticle are then calculated by point estimates. An example of this is
given in [32]. Estimates for the density standard deviation of polystyrene beads based
on data reported in [41] are provided in Table 5.1. The density standard deviation
from one yeast dataset was estimated to be 0.024 g/mL.
1st Mode
2nd Mode
Style
Population
Trapping
Population
Trapping
3µm
4µm
5µm
8.4959E-4 6.5061E-4 6.0606E-4
7.1233E-4 3.4825E-4 2.1840E-4
0.0012
9.3800E-4 8.4979E-4
2.657E-4 1.1937E-4 7.0493E-4
Table 5.1: Density variation estimates for 3, 4, and 5 µm diameter
polystyrene beads. The population-style measurements include data for hundreds
of particles and provide an upper estimate for density variation across polystyrene
beads. Density variation is theoretically zero for trapping (one particle measured hundreds of times), and these data provide an estimate of the error in the measurement
and accuracy of the calculation. Second mode operation (See [41] for more details)
eliminates position dependent error (see §5.8) and reduces peak height determination
error. The correlation coefficient was 1 for all calculations and deviation from 1 affected the reported density variation more significantly than observed in calculations
for cells.
5.5
Post-fabrication KOH etch for silicon microchannels
In order to measure cells without size biasing and reduce clogging, we developed a
method to increase the size of the cantilever microchannel post-fabrication. Potassium hydroxide, KOH, is an anisotropic wet etchant for silicon that can be delivered
to the cantilever in the same way as other fluidic samples. Once KOH is delivered and
heated, the cantilever’s silicon walls are etched internally and the total mass of the
cantilever decreases. The change in resonance frequency, however, is not directly proportional to this change in mass (Fig 5-3). Instead, the cantilever stiffness decreases
concurrently and resonance frequency is observed to decrease during sustained etch93
ing, which is consistent with the equation for natural resonance frequency:
1
f0 =
2π
r
k
,
m∗
(5.4)
where f0 is the resonant frequency, k is the cantilever stiffness, and m∗ is the effective
mass of the cantilever. In addition to accomodating larger cells, the mass reduction
during etching results in increased cantilever mass sensitivity (Fig 5-2, Table 5.2),
albeit a very small increased sensitivity for particle measurements.
Figure 5-2: Fluid density calibration with glycerol solutions before and after KOH
etching. This KOH etching procedure increases the fluid density sensitivity by ∼2fold.
Since the etch is crystal plane dependent, it disproportionately increases the cantilever channel entrance and reduces the cantilever microchannel’s dividing wall. The
increased entrance size can reduce clogging, but the accelerated etch of microchannel dividing wall introduces more position-dependent error (See §5.8). In the etch
described by Table 5.2, the coefficient of variation measured for 1.96 µm polystyrene
beads increased by ∼40% after etching! Careful consideration should be given to the
tradeoff between increased channel size and increased position-dependent error. No
more than 1 µm should be considered for etching as the microchannel may be offcenter in the vertical direction (expected lid thickness: ∼2µm) and further etching
94
will cause fluid leakage and vacuum loss.
KOH Etching Procedure. 25-45% KOH solution was loaded into the system
via syringe pump (15 µL/min). Etching is very slow at room temperature, so once
loaded the system was heated to 30-40◦ C. Temperature and resonance frequency (Fig
5-3) were recorded via a thermistor and frequency counter (HP 53131A), respectively.
Etching was stopped by quickly flushing the system with water once the resonance
frequency decreased by a desired few kilohertz. The laser for frequency readout was
periodically realigned because the cantilever stiffness, and therefore the cantilever’s
neutral position, was altered during the etching procedure.
Figure 5-3: Frequency response during post-fabrication KOH etching of an 8x8µm
cantilever. After the initial filling with 45% KOH (0-20 min), the temperature control
was set to 40◦ C. Resonance frequency increases as the silicon mass is replaced by KOH
solution, but then decreases as cantilever stiffnessrapidly decreases (Eqn 5.4).
In order to characterize the rate at which the etching occurs, we calculated the
cantilever volume before and after etching with a fluid density and point mass calibration (details in Table 5.2 caption). Assuming very little silicon is etched before
the temperature reaches 30◦ C, the etch rate is ∼2.25
µm/h
and expected to be faster
for higher temperatures. A second application for cantilever etching is described in
§3.1 to selectively change the resonance frequency of one cantilever in a two cantilever
system.
95
Before Etch
After Etch
Theory, Before Etch
Fluid Density
Calib. (Hz/g/mL)
Point Mass
Calib. Hz/pg
Dist. Mass
Calib. Hz/pg
23701
41102
3.14
3.39
0.7536
0.8136
Channel
Volume
Width
(µm3 )
(µm)
31450
8.61
50518
10.86
27072
8.00
Table 5.2: Calibrations and cantilever geometry before and after KOH etch.
KOH etching improves cantilever mass sensitivity and fluid density and point mass
calibrations can calculate etch rate. A three-point fluid density calibration (shown in
Fig 5-2) was performed with glycerol solutions, point mass calibration was performed
with 1.96 µm polystyrene beads, and the distributed mass calibration is 0.24·point
mass calibration. The cantilever volume is the quotient of the fluid density calibration
and distributed mass calibration. The theoretical channel width is calculated for an
8x8µm cross section, 209µm long cantilever, and 5µm wide channel dividing wall.
The channel width before and after etching are calculated based on this geometry.
5.6
SMR fluidic control to eliminate size biasing
The SMR channel geometry creates a bifurcation at which the cell may enter the
cantilever microchannel or continue down the bypass channel (Fig 5-4). Particle
behavior at bifurcations, the Zweifach-Fung effect [24], was initially believed to be
dictated solely by fluid flow rates, but the introduction of microfluidics and simulations have presented more complicated behavior [20, 8]. Particles likely enter the
channel of higher flow rate because of the distribution of particles across the parent
channel. Cells’ elastic properties promote migration to the center of the channel and
create a particle-free region near the wall, and the width of this particle-free region
is in part dictated by particle size. Thus, there is not only a flow rate-, but a sizedependency for the degree to which particles enter the cantilever microchannel. This
phenomenon has been directly observed in the SMR by measuring polystyrene beads
of equal concentration, but different size (Figure 2 from Ref [27]), and is exaggerated
with time as particles settle in the system.
Since the rate at which particles entering the cantilever microchannel is size dependent, severe biasing of the measured buoyant mass distribution can occur (Fig
5-5). One way to circumvent biasing is to flush the sample bypass channel at reg96
Figure 5-4: A cell travelling down the SMR bypass channel either enters the cantilever
microchannel or continues down the bypass channel, depending on fluid flow rates and
particle distribution in the bypass channel. The position of the separating streamline
(dashed line) is dictated by the fluid flow rates. If the bypass channel is fast compared
to that of the cantilever microchannel, the separating streamline nears the wall and
large particles will rarely enter the cantilever. Adapted from [20].
Figure 5-5: Volume distributions of a yeast cell population before (red line) and after
(green line) the SMR as measured by a Coulter counter. The “before” sample is from
the tube delivered to the SMR and the “after” sample is from a microcentrifuge tube
in the downstream waste vial (controlled by P3 in Fig 1-3).
97
ular intervals (every 1-4 minutes). This gently disturbs particles that have stuck or
otherwise settled in the microfluidic tubing, redistributes particles across the parent
channel, and allows for fresh sample to be carried to the vicinity of the cantilever.
Another approach to reduce size biasing is “pinched flow,” or feeding the cantilever
microchannel from both sides of the bypass channel and completely removing the separating streamline (Fig 5-4). Formation of pinched flow requires a microscope and fine
pressure adjustment by changing the fluid height, but has a secondary advantage—it
significantly reduces position dependent error (See §5.8) by flow-focusing.
5.7
Choice of a biologically-compatible high density medium
Closely matching the fluid density to that of a cell is complicated by the cell membrane, which can be permeable to high density materials and cause changes to cell
density. Heavy water and salt solutions (calcium chloride is ideal because of its
extreme hygroscopic properties) have both been used for measuring the density of
polystyrene beads with the SMR and with high accuracy. These solutions also function for other bead materials, and §3.4.1 describes how fluid density affects measurement accuracy for various particle densities. These fluids do not alter bead density,
but cells in heavy water rapidly alter their density as the heavy water exchanges with
intracellular water. Additionally, changes to solution tonicity, the concentration of
particles in solution that are not able to freely pass through a cell membrane (such as
certain ions), will cause rapid volume (and thus density) changes to the cell. Changes
to tonicity are often more relevant than osmolarity, the concentration of particles in
solution.
Aside from sucrose and high salt gradients, there are two commercial density gradient materials: colloidal silica (Percoll) and iodinated compounds (Histodenz/Nycodenz,
OptiPrep). Percoll is a silica colloid made with polyvinylpyrrolidone (PVP), which
reduces aggregation between the 15-30 nm silica particles and renders them non-toxic
98
[50]. The density of Percoll is 1.130 g/mL and the osmolality is 20 mOsmoles/kg H2 O,
compared to 250-300 mOsm/kg H2 O for cell media. Since solution tonicity is essentially independent of Percoll concentration, Percoll medium may be formulated with
powdered or concentrated medium by using Percoll in place of water. Brief exposure
to Percoll does not affect cell function [50], and there has been one case [21] where
some Percoll was observed inside of cells and did not alter cell density. Footnote 1
in §4.3 describes a freezing procedure to formulate higher density Percoll. Another
commercial density compound is OptiPrep, a dimer version of Histodenz/Nycodenz,
that derives its high density from iodine. OptiPrep has a maximum density of 1.32
g/mL,
but contributes to tonicity. A 50% solution of OptiPrep is approximately 195
mOsmoles/kg H2 O [2] and would create a hypertonic solution if made into medium.
The manufacturer reports that the solution is not metabolized by cells and that cells
can successfully grow in 5% OptiPrep with no change in viability compared to control
[23].
In the single-cell mass, density, and volume methods described in Chapters 3
and 4, cells spend ∼3-5 seconds in the high density medium, which is only enough
time for an osmotic response. Since these population-style methods do not require
longer term measurements, we selected Percoll for its low osmolarity and did not
investigate other effects of exposure to high density materials. A long term singlecell density measurement, in contrast to the methods presented here, would require
repeated exposure of the cell to high density material and may activate stress response
pathways that could cause the cell’s mass, density, and volume to respond in a way
that is not observed in a cell without exposure. Stress pathway signaling as measured
by p38/Hog1 can occur in as little as 10 seconds, but how quickly this affects mass
and density is not known. An initial measure of the effects of Percoll medium on cell
growth would be to measure culture doubling time, cell volume distributions, and
microarray analysis of key stress response pathways for cells cultured in high density
medium for different concentrations and lengths of time.
99
Figure 5-6: Illustration of SMR position-dependent error (A)A particle in the
SMR may transit anywhere between the inner and outer channel wall. A particle that
makes a U-turn near the inner wall (dashed green line) causes a smaller frequency
shift than if it turns near the outer wall (solid red line). (B) Resonance frequency
shifts upon point mass loading on a cantilever as a function of the position of the
added mass normalized by the cantilever length.
5.8
SMR particle position-dependent error
When a particle flows through the resonator’s microchannel the resonance frequency
shift is position-dependent, with the maximum frequency shift occurring when the
particle is at the SMR tip. Since the microchannel width is designed to accommodate a range of particle sizes and reduce clogging, the particle flow path near the
tip of the SMR is uncertain and reduces the precision of the mass measurement (Fig
5-6). This position-dependent error can broaden the measured mass histogram of
a population of particles and introduce additional uncertainty during single particle trapping [28]. This error was briefly addressed in our previous work [16], but
there has been little effort to quantify the position-dependent error experimentally
and explore methods that reduce this error. Here, we quantify position-dependent
error inherent in particle mass sensing with the SMR and discuss solutions that can
eliminate position-dependent error without sacrificing throughput. As shown in Fig
5-6, a particle flowing through the embedded microchannel of the SMR can travel
along random paths. In the most extreme case, the particle can be positioned at the
inner or outer edge of the microchannel. Since the buoyant mass of a particle is small
relative to the total cantilever mass, the maximum position-dependent error can be
100
estimated by:
u(xi /l)2 − u(xo /l)2
fi − fo
≈
,
f − fm
u(xm /l)2
(5.5)
where f is the resonance frequency, x is the particle position, l is the cantilever length,
the subscripts i, o, and, m denote particle positions at the inner edge, the outer edge,
and the midpoint of the channel, respectively, and where u is the normalized beam
displacement (Fig 5-7A) given by:
u
x
l
x
x x
x = B 0 cos κ
− cosh κ
+ D0 sin κ
− sinh κ
,
l
l
l
l
(5.6)
for which κ is 1.875 and D’/B’ is -0.7341 for the first mode of vibration [60] (further
details provided in [41]). Whereas the system noise level is an absolute uncertainty
and determines the minimum detectable mass, the position error determines the resolution at which particles having similar buoyant masses can be differentiated. This
error is linearly proportional to particle diameter (Fig 5-7B) and, if not normalized,
the error is also proportional to particle buoyant mass (data not shown). Thus, depending on the particle’s properties, the uncertainty may not be negligible compared
to the system frequency resolution.
Perfectly monodispersed particles would be ideal for experimentally quantifying
position-dependent error because particle size dispersity may overshadow positiondependent error in population measurements. Typical coefficient of variations (CVs)
of commercially available NIST size standard beads are 1-2% in diameter, which are
comparable to the position-dependent error. We therefore used a dynamic single
particle trapping method where we alternated the pressure between the SMR bypass
channels to maintain a single particle in the suspended microchannel for repeated
measurements [28]. The buoyant mass CV measured by single particle trapping for
a 3 µm diameter polystyrene bead is 1.40%, which is less than the 1.76% observed
for a population measurement (Fig 5-8). Measured CVs can be greater than that
predicted by the theory because of errors in peak height determination, or less than
that predicted by the theory because of unintentional flow focusing during trapping.
As particle diameter increases, the disparity between these two CVs also increases.
101
Figure 5-7: Simulations for position dependent error. (A) Cantilever deflection
as a function of length. (B) Position-dependent error relative to channel middle as
a function of particle diameter for 8x8µm and 15x20µm SMR designs. As particle
diameter approaches the channel width, the position dependent error linearly decreases. Smaller cantilevers have decreased position-dependent error as compared to
larger cantilevers for the same size particle. (C) Position dependent error decreases
nonlinearly with cantilever length, but there is a tradeoff between decreased positiondependent error and decreased mass sensitivity (as a result of increased cantilever
mass) that must be considered in cantilever design.
102
Figure 5-8: Histograms of relative resonance frequency shifts (∆f/∆favg )
Data shown for nominally 3 µm diameter polystyrene particles (population; top)
and repeated measurements of a single particle drawn from the same population
(single particle trap; bottom). Measured histograms for a single trapped particle
are not affected by the size variation observed in populations, but are wider than or
comparable to the theoretical position-dependent error (given by two vertical dashed
lines) because of system frequency noise and the filter’s smoothing effect during data
processing.
103
One approach to reduce position-dependent error is to decrease cantilever length.
Position-dependent error decreases nonlinearly with cantilever length (Fig 5-7C), but
the resulting decreased mass sensitivity with added cantilever mass must be considered in cantilever design. A method to eliminate position dependent error with
existing SMR devices is to operate the cantilever’s second flexural bending modes to
achieve high precision mass sensing and, in some cases, provide improved mass resolution [41]. By eliminating position-dependent error, second mode antinode sensing
can lower the minimum detectable size dispersity in particle samples and potentially
reduce the time required for measuring single cell growth rates with dynamic trapping
[28].
It is also interesting to consider the utility of position-dependent error. If a trapped
particle travels random streamlines through the SMR, the normalized variation in
buoyant mass measurements will be directly proportional to the particle’s diameter.
Larger particles are not able to follow as many streamlines and produce a smaller
normalized variation in buoyant mass, and vice versa. This information may be used
to estimate particle volume, and therefore density, as a function of time. Although
this has been demonstrated for beads of different sizes (not shown), in practice it can
be difficult to trap single particles without some degree of hydrofocussing.
104
Chapter 6
Postscript
Integration of a resistive pulse (Coulter) measurement into the SMR buoyant mass
measurement system would simplify fluidic operation of a single-cell mass, volume,
and density measurement system. The single-cell density measurements presented in
this thesis require exchange of the fluid surrounding a cell. This fluid exchange is
nearly irreversible, and since a microfluidic environment is limited to laminar flow,
the exchange occurs by pure diffiusion. Diffusion requires long timescales for complete
mixing and small pressure fluctuations can alter the time allowed for diffusion. Thus,
in contrast to the density measurements that require two buoyant mass measurements
made in different density fluids (population: Reference [27], single-cell: Chapters 3
and 4), a buoyant mass measurement paired with volume datum (population: described in Chapter 2) is ideal for numerous reasons: it requires only one SMR, there
is no exposure to high density fluids, and there is greatly simplified fluidic operation.
Such a measurement may be achieved by pairing buoyant mass and volume data at
the single-cell level through a microfluidic SMR-Coulter device. Trapping single cells
[28] in such a device would enable mass, density, and volume properties to be tracked
as cells respond to environmental perturbations.
The Coulter principle measures changes in electrical impedance across a small pore
through which a particle passes. The development of microfluidic Coulter counters
began in 1997 and have used a variety of materials and measurement approaches
with varied success. The most recent implementation reports single-cell yeast volume
105
growth using MOSFET drain current detection [63], and measurements continue to
improve. Many of the limitations associated with a Coulter-style volume measurement
are caused by nonuniformities in the electric field within the aperture, which result in
shape and orientation-dependent measurements not present in the SMR. Additionally,
there are challenges in making electrical measurements in a silicon device. Although a
low-noise impedance-based volume measurement is a feat in and of itself, the pairing
of this with the current SMR system would be revolutionary.
106
Appendix A
Supplementary Figures
A.1
Chapter 2 Supplementary Figures
107
Figure A-1: Proportion of budded cells for Figure 2-4 measurements. Cells were
prepared as described in Figure 2-4, aliquots were fixed in formaldehyde at 10 minute
intervals, and bud counts were recorded after sample collection.
108
Figure A-2: Statistical analysis of continuous measurement shown in Figure
2-4. Volume data greater than 400 µm3 was excluded from analysis. (A) Calculated
mean of buoyant mass and volume measurements for each time division. (B) Coefficient of variation (CV) at each time division. Color designates the corresponding
time (color bar at right).
109
Figure A-3: Buoyant mass and volume of additional continuous measurement. Color designates the fraction of the population with the indicated buoyant
mass and volume (color bar at right). Cells were synchronized and measured as
described in Figure 2-4. (A) The SMR steadily sampled from the culture and measurements were broken into 10 minute divisions (N=11,210 cells). (B) Volume measurements on a split culture were made from aliquots drawn at 10 minute intervals
and recorded in <1min (N=39,695 cells). (C) Proportion of budded cells recorded
after formaldehyde fixation for each sample.
110
Figure A-4: Statistical analysis of continuous measurement shown in Supplemental Figure A-3. Volume data greater than 400 m3 was excluded from analysis.
(A) Calculated mean of buoyant mass and volume measurements for each time division. (B) Coefficient of variation (CV) at each time division. Color designates the
corresponding time (color bar at right).
111
Figure A-5: Bud emergence and DNA content analysis. WT cells (A2587)
were released into a synchronous cell cycle and treated with 100µM LatA or equal
volume DMSO, or 10µM rapamycin or equal volume 70% ethanol, as indicated. (A)
The number of budded cells was counted from formaldehyde-fixed aliquots of each
sample. Cells did not bud under either treatment. (B) Additional aliquots were
collected for flow cytometric analysis of DNA content. Both treatments have partial
DNA replication. (C) The FACS histograms in (B) were analyzed by the Watson
pragmatic model (FlowJo, Treestar, USA) to calculate the cell cycle distribution. The
number of cells with one DNA copy decreases as replication begins.
112
A.2
Chapter 3 Supplementary Figures
A
Cells in lessdense buffer
B
More-dense
buffer
Cells in lessdense buffer
SMR
Waste 1
C
More-dense
buffer
Cells in lessdense buffer
SMR
Waste 2
Waste 1
Solenoid
valves
D
More-dense
buffer
Cells in lessdense buffer
SMR
Waste 2
Waste 1
Solenoid
valves
More-dense
buffer
SMR
Waste 2
Waste 1
Solenoid
valves
Waste 2
Solenoid
valves
Vacuum
Vacuum
Vacuum
Vacuum
Pressure
Pressure
Pressure
Pressure
Figure A-6: Diagram of density measurement system. Briefly, a pressure differential
between two parallel fluid paths (red and blue) sends a single cell from the red path
through the resonating microchannel (SMR) and into the blue path. Once the buoyant
mass of the cell is measured in media (red), the fluid flow reverses direction to measure
the same cell in the alternate-density fluid (blue) and the system is reset. See Chapter
4 text for details.
113
14
12
p = 0.001
90
85
80
16
14
12
10
Normal Transfused
(n = 7) (n = 7)
G
p = 0.002
10
8
20
18
16
14
12
10
8
CV of erythrocyte
mass (%)
D
J
Normal Transfused
(n = 7) (n = 7)
p = 0.005
Normal Transfused
(n = 7) (n = 7)
Normal Transfused
(n = 7) (n = 7)
E
p = 0.001
Normal Transfused
(n = 7) (n = 7)
SD of erythrocyte
mass (pg)
16
14
12
10
IQR of erythrocyte
mass (pg)
IQR of erythrocyte
volume (fL)
SD of erythrocyte
volume (fL)
CV of erythrocyte
volume (%)
Normal Transfused
(n = 7) (n = 7)
p = 0.222
Mean erythrocyte
density (g/mL)
75
B
CV of erythrocyte
density (%)
80
95
14
H
p = 0.004
12
10
8
22
20
18
16
14
12
10
SD of erythrocyte
density (g/mL)
p = 0.222
Normal Transfused
(n = 7) (n = 7)
K
p = 0.008
Normal Transfused
(n = 7) (n = 7)
IQR of erythrocyte
density (g/mL)
A
Mean erythrocyte
mass (pg)
Mean erythrocyte
volume (fL)
85
1.110
C
p = 0.101
1.105
1.100
0.8
Normal Transfused
(n = 7) (n = 7)
F
p = 0.008
0.6
0.4
0.010
0.008
I
Normal Transfused
(n = 7) (n = 7)
p = 0.008
0.006
0.004
0.008
Normal Transfused
(n = 7) (n = 7)
L
p = 0.011
0.006
Normal Transfused
(n = 7) (n = 7)
Figure A-7: Additional statistical analysis of the erythrocyte mass, volume, and
density distributions for the seven recently-transfused individuals and seven nontransfused individuals from Figure 3. The patients’ mean erythrocyte volumes (A),
masses (B), and densities (C) are not significantly different between the normal and
transfused groups (p ¿ 0.01). The coefficients of variation (D, E, F), standard deviations (G, H, I), and interquartile ranges (J, K, L) of the patients’ erythrocyte volumes,
masses, and densities are significantly different between the normal and transfused
groups (p ¡ 0.01). P values are from the Mann-Whitney U test.
114
Mean cell Hb mass
from Siemens ADVIA (pg)
Mean cell volume
from Siemens ADVIA (fL)
100
95
Mean cell Hb concentration
from Siemens ADVIA (g/dL)
C
B
90
85
R2 = 0.68
80
34
R2 = 0.69
D
E
F
32
30
R2 = 0.74
28
36
Hematocrit
from Siemens ADVIA
A
35
R2 = 0.74
G
H
I
J
K
L
34
33
32
50
40
30
20
70
75 80 85
Mean cell volume
from SMR (fL)
90
80
85 90 95
Mean cell mass
from SMR (pg)
1.100
1.105
1.110
Mean cell density
from SMR (g/mL)
Figure A-8: Comparisons between parameters measured by the Siemens ADVIA clinical hematology instrument and parameters measured by our SMR, for the 14 individuals in Figure 3. Red points indicate recently-transfused individuals and black
points indicate non-transfused individuals. Both the ADVIA and the SMR measure
mean cell volume, and there is a reasonable correlation between the mean volumes
measured by the two instruments (A). Similar correlations exist between the mean
cell volume from the ADVIA and the mean cell mass from the SMR (B). Additional
correlations can be found between the mean cell hemoglobin (Hb) mass from the
ADVIA and the mean cell volume and mass from the SMR (D, E). However, mean
cell hemoglobin concentration and hematocrit from the ADVIA did not obviously
correlate with mean cell volume or mass from the SMR (G, H, J, K). In addition, cell
density from the SMR did not correlate with any of the ADVIA’s measurements (C,
F, I, L), suggesting that the factors that determine erythrocyte density are not merely
115
a function of the cell’s size or hemoglobin content, or an individual’s hematocrit.
A
STD of cell volume
from Siemens ADVIA (fL)
CV of cell volume
from Siemens ADVIA (%)
18
17
16
15
14
13
12
11
10
R2 = 0.61
8
10 12 14 16
CV of cell volume
from SMR (%)
18
17
16
15
14
13
12
11
10
9
B
R2 = 0.46
6
8 10 12 14
STD of cell volume
from SMR (fL)
16
Figure A-9: Comparisons between the distribution widths of erythrocyte volumes
(RDW) measured by the Siemens ADVIA and our SMR, for the 14 individuals in
Figure 3, measured as either coefficient of variation (A) or standard deviation (B).
Red points indicate recently-transfused individuals and black points indicate nontransfused individuals. Both the coefficient of variation (A) and the standard deviation (B) of the individuals’ erythrocyte volumes agree well between the ADVIA and
SMR instruments (with the exception of one possible outlier).
116
12
R2 = 1.00
10
14
12
12
10
8
R2 = 1.00
8 10 12 14
STD of cell volume (fL)
16
14
12
12
10
8
R2 = 0.57
R2 = 0.64
10
0.4
0.6
0.8
CV of cell density (%)
16
E
C
14
0.4
0.6
0.8
CV of cell density (%)
STD of cell volume (fL)
STD of cell mass (pg)
14
D
R2 = 0.65
10
10 12 14 16
CV of cell volume (%)
16
B
CV of cell mass (%)
14
16
STD of cell mass (pg)
A
CV of cell volume (%)
CV of cell mass (%)
16
0.004 0.006 0.008 0.010
STD of cell density (g/mL)
14
F
12
10
8
R2 = 0.56
0.004 0.006 0.008 0.010
STD of cell density (g/mL)
Figure A-10: Correlations among the distribution widths of erythrocyte volumes,
masses, and densities measured by the SMR, for the 14 individuals in Figure 3, measured as either coefficient of variation (A, B, C) or standard deviation (D, E, F).
Red points indicate recently-transfused individuals and black points indicate nontransfused individuals. The distribution widths of the erythrocyte masses and volumes correlate extremely well with each other (A, D), though density distribution
only moderately correlates with volume distribution and mass distribution (B, C, E,
F). This suggests that an individual with an increased volume variability (RDW)
likely will have increased mass and density variability as well, though the density
variability is not solely a function of the other two variabilities.
117
Figure A-11: Analysis of repeated blood draws from the transfused thalassemia patient in Figure 2D.
118
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Invest a few moments in thinking.
It will pay good interest.
-Anonymous
125